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Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-19 Quirin Aumann, Steffen W. R. Werner
Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal interpolation points and the appropriate size of the reduced-order model. An approach that addresses the first problem for linear, unstructured systems is the iterative
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Quantitative Stability of the Pushforward Operation by an Optimal Transport Map Found. Comput. Math. (IF 2.5) Pub Date : 2024-07-19 Guillaume Carlier, Alex Delalande, Quentin Mérigot
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On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-19 Kui Du, Jia-Jun Fan, Xiao-Hui Sun, Fang Wang, Ya-Lan Zhang
Krylov subspace methods for solving linear systems of equations involving skew-symmetric matrices have gained recent attention. Numerical equivalences among Krylov subspace methods for nonsingular skew-symmetric linear systems have been given in Greif et al. [SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1071–1087]. In this work, we extend the results of Greif et al. to singular skew-symmetric linear
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A continuation method for fitting a bandlimited curve to points in the plane Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-16 Mohan Zhao, Kirill Serkh
In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in \(\mathbb {R}^{2}\). The main idea is to smooth the parametrization of the curve by iteratively filtering the Fourier or Chebyshev coefficients of both the derivative of the arc-length function and the tangential angle of the curve and applying smooth
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Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-16 Hong Zhu, Xiaoxia Liu, Lin Huang, Zhaosong Lu, Jian Lu, Michael K. Ng
Multi-dimensional images can be viewed as tensors and have often embedded a low-rankness property that can be evaluated by tensor low-rank measures. In this paper, we first introduce a tensor low-rank and sparsity measure and then propose low-rank and sparsity models for tensor completion, tensor robust principal component analysis, and tensor denoising. The resulting tensor recovery models are further
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Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-16 Julian Koellermeier, Philipp Krah, Jonas Kusch
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques that allow for efficient and accurate simulations while guaranteeing physical properties like mass conservation. In this paper, we develop the first model reduction
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Finding roots of complex analytic functions via generalized colleague matrices Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-15 H. Zhang, V. Rokhlin
We present a scheme for finding all roots of an analytic function in a square domain in the complex plane. The scheme can be viewed as a generalization of the classical approach to finding roots of a function on the real line, by first approximating it by a polynomial in the Chebyshev basis, followed by diagonalizing the so-called “colleague matrices.” Our extension of the classical approach is based
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Neural and spectral operator surrogates: unified construction and expression rate bounds Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-15 Lukas Herrmann, Christoph Schwab, Jakob Zech
Approximation rates are analyzed for deep surrogates of maps between infinite-dimensional function spaces, arising, e.g., as data-to-solution maps of linear and nonlinear partial differential equations. Specifically, we study approximation rates for deep neural operator and generalized polynomial chaos (gpc) Operator surrogates for nonlinear, holomorphic maps between infinite-dimensional, separable
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Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-15 Fengshan Zhang, Yongkui Zou, Shimin Chai, Yanzhao Cao
In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up
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A sparse spectral method for fractional differential equations in one-spatial dimension Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-10 Ioannis P. A. Papadopoulos, Sheehan Olver
We develop a sparse spectral method for a class of fractional differential equations, posed on \(\mathbb {R}\), in one dimension. These equations may include sqrt-Laplacian, Hilbert, derivative, and identity terms. The numerical method utilizes a basis consisting of weighted Chebyshev polynomials of the second kind in conjunction with their Hilbert transforms. The former functions are supported on
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Pairwise ranking with Gaussian kernel Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-10 Guanhang Lei, Lei Shi
Regularized pairwise ranking with Gaussian kernels is one of the cutting-edge learning algorithms. Despite a wide range of applications, a rigorous theoretical demonstration still lacks to support the performance of such ranking estimators. This work aims to fill this gap by developing novel oracle inequalities for regularized pairwise ranking. With the help of these oracle inequalities, we derive
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Topological phase estimation method for reparameterized periodic functions Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-08 Thomas Bonis, Frédéric Chazal, Bertrand Michel, Wojciech Reise
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An adaptive finite element DtN method for the acoustic-elastic interaction problem Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-08 Lei Lin, Junliang Lv, Shuxin Li
Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable and isotropic elastic solid, which is immersed in a homogeneous compressible air/fluid. By the Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition is introduced and the model is formulated as a boundary value problem of acoustic-elastic interaction. Based on a duality argument technique
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Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-08 Guidong Liu, Wenjie Liu, Beiping Duan
In this paper, optimal estimates on the decaying rates of Jacobi expansion coefficients are obtained by fractional calculus for functions with algebraic and logarithmic singularities. This is inspired by the fact that integer-order derivatives fail to deal with singularity of fractional-type, while fractional calculus can. To this end, we first introduce new fractional Sobolev spaces defined as the
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On an accurate numerical integration for the triangular and tetrahedral spectral finite elements Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-03 Ziqing Xie, Shangyou Zhang
In the triangular/tetrahedral spectral finite elements, we apply a bilinear/trilinear transformation to map a reference square/cube to a triangle/tetrahedron, which consequently maps the \(\varvec{Q_k}\) polynomial space on the reference element to a finite element space of rational/algebraic functions on the triangle/tetrahedron. We prove that the resulting finite element space, even under this singular
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An adaptive time-stepping Fourier pseudo-spectral method for the Zakharov-Rubenchik equation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-03 Bingquan Ji, Xuanxuan Zhou
An adaptive time-stepping scheme is developed for the Zakharov-Rubenchik system to resolve the multiple time scales accurately and to improve the computational efficiency during long-time simulations. The Crank-Nicolson formula and the Fourier pseudo-spectral method are respectively utilized for the temporal and spatial approximations. The proposed numerical method is proved to preserve the mass and
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Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-03 Terrence Alsup, Tucker Hartland, Benjamin Peherstorfer, Noemi Petra
Multilevel Stein variational gradient descent is a method for particle-based variational inference that leverages hierarchies of surrogate target distributions with varying costs and fidelity to computationally speed up inference. The contribution of this work is twofold. First, an extension of a previous cost complexity analysis is presented that applies even when the exponential convergence rate
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Extrapolated regularization of nearly singular integrals on surfaces Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-01 J. Thomas Beale, Svetlana Tlupova
We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or Stokes flow, are evaluated at points nearby. Such values could be needed in solving an integral equation when one surface is close to another or to obtain values at grid points. We replace the singular kernel with a regularized version having a length parameter
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Convergence of projected subgradient method with sparse or low-rank constraints Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-02 Hang Xu, Song Li, Junhong Lin
Many problems in data science can be treated as recovering structural signals from a set of linear measurements, sometimes perturbed by dense noise or sparse corruptions. In this paper, we develop a unified framework of considering a nonsmooth formulation with sparse or low-rank constraint for meeting the challenges of mixed noises—bounded noise and sparse noise. We show that the nonsmooth formulations
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Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data Adv. Comput. Math. (IF 1.7) Pub Date : 2024-06-24 Martin Hanke
We consider the problem of constructing a vector-valued linear Markov process in continuous time, such that its first coordinate is in good agreement with given samples of the scalar autocorrelation function of an otherwise unknown stationary Gaussian process. This problem has intimate connections to the computation of a passive reduced model of a deterministic time-invariant linear system from given
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On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-06-18 Bing Tan, Xiaolong Qin
We present three novel algorithms based on the forward-backward splitting technique for the solution of monotone inclusion problems in real Hilbert spaces. The proposed algorithms work adaptively in the absence of the Lipschitz constant of the single-valued operator involved thanks to the fact that there is a non-monotonic step size criterion used. The weak and strong convergence and the R-linear convergence
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Koszul Complexes and Relative Homological Algebra of Functors Over Posets Found. Comput. Math. (IF 2.5) Pub Date : 2024-06-18 Wojciech Chachólski, Andrea Guidolin, Isaac Ren, Martina Scolamiero, Francesca Tombari
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A Local Nearly Linearly Convergent First-Order Method for Nonsmooth Functions with Quadratic Growth Found. Comput. Math. (IF 2.5) Pub Date : 2024-06-14 Damek Davis, Liwei Jiang
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An efficient rotational pressure-correction schemes for 2D/3D closed-loop geothermal system Adv. Comput. Math. (IF 1.7) Pub Date : 2024-06-10 Jian Li, Jiawei Gao, Yi Qin
In this paper, the rotational pressure-correction schemes for the closed-loop geothermal system are developed and analyzed. The primary benefit of this projection method is to replace the incompressible condition. The system is considered consisting of two distinct regions, with the free flow region governed by the Navier–Stokes equations and the porous media region governed by Darcy’s law. At the
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Numerical methods for forward fractional Feynman–Kac equation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-06-10 Daxin Nie, Jing Sun, Weihua Deng
Fractional Feynman–Kac equation governs the functional distribution of the trajectories of anomalous diffusion. The non-commutativity of the integral fractional Laplacian and time-space coupled fractional substantial derivative, i.e., \(\mathcal {A}^{s}{}_{0}\partial _{t}^{1-\alpha ,x}\ne {}_{0}\partial _{t}^{1-\alpha ,x}\mathcal {A}^{s}\), brings about huge challenges on the regularity and spatial
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Convergent Regularization in Inverse Problems and Linear Plug-and-Play Denoisers Found. Comput. Math. (IF 2.5) Pub Date : 2024-06-03 Andreas Hauptmann, Subhadip Mukherjee, Carola-Bibiane Schönlieb, Ferdia Sherry
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Semi-active damping optimization of vibrational systems using the reduced basis method Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-31 Jennifer Przybilla, Igor Pontes Duff, Peter Benner
In this article, we consider vibrational systems with semi-active damping that are described by a second-order model. In order to minimize the influence of external inputs to the system response, we are optimizing some damping values. As minimization criterion, we evaluate the energy response, that is the \(\mathcal {H}_2\)-norm of the corresponding transfer function of the system. Computing the energy
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A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-30 Meiting Wang, Guang-an Zou, Jian Li
This paper is devoted to the numerical approximations of the Cahn-Hilliard-Darcy-Stokes system, which is a combination of the modified Cahn-Hilliard equation with the Darcy-Stokes equation. A novel discontinuous Galerkin pressure-correction scheme is proposed for solving the coupled system, which can achieve the desired level of linear, fully decoupled, and unconditionally energy stable. The developed
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Identifiability, the KL Property in Metric Spaces, and Subgradient Curves Found. Comput. Math. (IF 2.5) Pub Date : 2024-05-28 A. S. Lewis, Tonghua Tian
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Approximation in the extended functional tensor train format Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-28 Christoph Strössner, Bonan Sun, Daniel Kressner
This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank approximation algorithm that is entirely based on function evaluations. Compared to existing methods based on the functional tensor train format, the adaptivity of
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An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-22 Fanyi Yang, Xiaoping Xie
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An optimal control framework for adaptive neural ODEs Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-23 Joubine Aghili, Olga Mula
In recent years, the notion of neural ODEs has connected deep learning with the field of ODEs and optimal control. In this setting, neural networks are defined as the mapping induced by the corresponding time-discretization scheme of a given ODE. The learning task consists in finding the ODE parameters as the optimal values of a sampled loss minimization problem. In the limit of infinite time steps
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Variable transformations in combination with wavelets and ANOVA for high-dimensional approximation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-23 Daniel Potts, Laura Weidensager
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation, we are able to transform the approximation rates and fast algorithms from the torus to other domains. We perform
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Optimal Approximation of Unique Continuation Found. Comput. Math. (IF 2.5) Pub Date : 2024-05-20 Erik Burman, Mihai Nechita, Lauri Oksanen
We consider numerical approximations of ill-posed elliptic problems with conditional stability. The notion of optimal error estimates is defined including both convergence with respect to discretisation and perturbations in data. The rate of convergence is determined by the conditional stability of the underlying continuous problem and the polynomial order of the approximation space. A proof is given
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Error analysis of a collocation method on graded meshes for a fractional Laplacian problem Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-20 Minghua Chen, Weihua Deng, Chao Min, Jiankang Shi, Martin Stynes
The numerical solution of a 1D fractional Laplacian boundary value problem is studied. Although the fractional Laplacian is one of the most important and prominent nonlocal operators, its numerical analysis is challenging, partly because the problem’s solution has in general a weak singularity at the boundary of the domain. To solve the problem numerically, we use piecewise linear collocation on a
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A sparse approximation for fractional Fourier transform Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-20 Fang Yang, Jiecheng Chen, Tao Qian, Jiman Zhao
The paper promotes a new sparse approximation for fractional Fourier transform, which is based on adaptive Fourier decomposition in Hardy-Hilbert space on the upper half-plane. Under this methodology, the local polynomial Fourier transform characterization of Hardy space is established, which is an analog of the Paley-Wiener theorem. Meanwhile, a sparse fractional Fourier series for chirp \( L^2 \)
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Group-Invariant Max Filtering Found. Comput. Math. (IF 2.5) Pub Date : 2024-05-17 Jameson Cahill, Joseph W. Iverson, Dustin G. Mixon, Daniel Packer
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A Sheaf-Theoretic Construction of Shape Space Found. Comput. Math. (IF 2.5) Pub Date : 2024-05-16 Shreya Arya, Justin Curry, Sayan Mukherjee
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An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-15 Marco Bernreuther, Stefan Volkwein
In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator is adopted to the presence of the discrete empirical interpolation method (DEIM) as approximation technique for the nonsmoothness. The separability of the estimated
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A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-08 Marta Benítez, Alfredo Bermúdez, Pedro Fontán, Iván Martínez, Pilar Salgado
The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry varies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermo-electromagnetic-mechanical model suitable for simulating electrically assisted forming processes
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Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-08 Xinyue Gao, Yi Qin, Jian Li
In this paper, a new time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise is developed and studied. This model considers heat transfer between the free flow in the pipe region and the porous media flow in the porous media region. Darcy’s law and stochastic Navier-Stokes equations are used to control the flows in the pipe and porous media regions, respectively. The
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Local behaviors of Fourier expansions for functions of limited regularities Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-09 Shunfeng Yang, Shuhuang Xiang
Based on the explicit formula of the pointwise error of Fourier projection approximation and by applying van der Corput-type Lemma, optimal convergence rates for periodic functions with different degrees of smoothness are established. It shows that the convergence rate enjoys a decay rate one order higher in the smooth parts than that at the singularities. In addition, it also depends on the distance
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Anita T. Layton
SIAM Review, Volume 66, Issue 2, Page 391-399, May 2024. As I sat down to write this introduction, I became curious how the books chosen for review have changed over the past decades. So I scanned through a few SIREV Book Review section introductions written 10, 20 or more years ago by former section editors. That act of procrastination allows me to put the current collection of reviews in “historical
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Dynamics of Signaling Games SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Hannelore De Silva, Karl Sigmund
SIAM Review, Volume 66, Issue 2, Page 368-387, May 2024. This tutorial describes several basic and much-studied types of interactions with incomplete information, analyzing them by means of evolutionary game dynamics. The games include sender-receiver games, owner-challenger contests, costly advertising, and calls for help. We model the evolution of populations of players reacting to each other and
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The Poincaré Metric and the Bergman Theory SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Steven G. Krantz
SIAM Review, Volume 66, Issue 2, Page 355-367, May 2024. We treat the Poincaré metric on the disc. In particular we emphasize the fact that it is the canonical holomorphically invariant metric on the unit disc. Then we generalize these ideas to the Bergman metric on a domain in complex space. Along the way we treat the Bergman kernel and study its invariance and uniqueness properties.
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Education SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Hélène Frankowska
SIAM Review, Volume 66, Issue 2, Page 353-353, May 2024. In this issue the Education section presents two contributions. The first paper, “The Poincaré Metric and the Bergman Theory,” by Steven G. Krantz, discusses the Poincaré metric on the unit disc in the complex space and the Bergman metric on an arbitrary domain in any dimensional complex space. To define the Bergman metric the notion of Bergman
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Nonsmooth Optimization over the Stiefel Manifold and Beyond: Proximal Gradient Method and Recent Variants SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Shixiang Chen, Shiqian Ma, Anthony Man-Cho So, Tong Zhang
SIAM Review, Volume 66, Issue 2, Page 319-352, May 2024. We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this class of problems converge slowly in practice, involve subproblems that can be as difficult as the original problem, or lack rigorous convergence guarantees. In
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SIGEST SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 The Editors
SIAM Review, Volume 66, Issue 2, Page 317-317, May 2024. The SIGEST article in this issue is “Nonsmooth Optimization over the Stiefel Manifold and Beyond: Proximal Gradient Method and Recent Variants,” by Shixiang Chen, Shiqian Ma, Anthony Man-Cho So, and Tong Zhang. This work considers nonsmooth optimization on the Stiefel manifold, the manifold of orthonormal $k$-frames in $\mathbb{R}^n$. The authors
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A New Version of the Adaptive Fast Gauss Transform for Discrete and Continuous Sources SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Leslie F. Greengard, Shidong Jiang, Manas Rachh, Jun Wang
SIAM Review, Volume 66, Issue 2, Page 287-315, May 2024. We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave representation of the Gaussian kernel and a new hierarchical merging scheme. For continuous source distributions sampled on adaptive tensor product grids, we exploit
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Research Spotlights SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Stefan M. Wild
SIAM Review, Volume 66, Issue 2, Page 285-285, May 2024. The Gauss transform---convolution with a Gaussian in the continuous case and the sum of $N$ Gaussians at $M$ points in the discrete case---is ubiquitous in applied mathematics, from solving ordinary and partial differential equations to probability density estimation to science applications in astrophysics, image processing, quantum mechanics
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Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection Methods SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Julianne Chung, Silvia Gazzola
SIAM Review, Volume 66, Issue 2, Page 205-284, May 2024. This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the numerical linear algebra community and have proved important in solving inverse problems due to their inherent
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Survey and Review SIAM Rev. (IF 10.8) Pub Date : 2024-05-09 Marlis Hochbruck
SIAM Review, Volume 66, Issue 2, Page 203-203, May 2024. Inverse problems arise in various applications---for instance, in geoscience, biomedical science, or mining engineering, to mention just a few. The purpose is to recover an object or phenomenon from measured data which is typically subject to noise. The article “Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection
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On the maximum principle and high-order, delay-free integrators for the viscous Cahn–Hilliard equation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-03 Hong Zhang, Gengen Zhang, Ziyuan Liu, Xu Qian, Songhe Song
The stabilization approach has been known to permit large time-step sizes while maintaining stability. However, it may “slow down the convergence rate” or cause “delayed convergence” if the time-step rescaling is not well resolved. By considering a fourth-order-in-space viscous Cahn–Hilliard (VCH) equation, we propose a class of up to the fourth-order single-step methods that are able to capture the
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Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-03 Pawan Goyal, Igor Pontes Duff, Peter Benner
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial functions, and the linear part corresponds to a linear structured model, such as second-order, time-delay, or fractional-order systems. Our approach relies on the Volterra
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Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-06 Huaijun Yang, Meng Li
In this paper, a linearized structure-preserving Galerkin finite element method is investigated for Poisson-Nernst-Planck (PNP) equations. By making full use of the high accuracy estimation of the bilinear element, the mean value technique and rigorously dealing with the coupled nonlinear term, not only the unconditionally optimal error estimate in \(L^2\)-norm but also the unconditionally superclose
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Stray field computation by inverted finite elements: a new method in micromagnetic simulations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-07 Tahar Z. Boulmezaoud, Keltoum Kaliche
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Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-02 Louis Lamérand, Didier Auroux, Philippe Ghendrih, Francesca Rapetti, Eric Serre
Two-dimensional transport codes for the simulation of tokamak plasma are reduced version of full 3D fluid models where plasma turbulence has been smoothed out by averaging. One of the main issues nowadays in such reduced models is the accurate modelling of transverse transport fluxes resulting from the averaging of stresses due to fluctuations. Transverse fluxes are assumed driven by local gradients
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Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-02 David Berghaus, Robert Stephen Jones, Hartmut Monien, Danylo Radchenko
We numerically compute the lowest Laplacian eigenvalues of several two-dimensional shapes with dihedral symmetry at arbitrary precision arithmetic. Our approach is based on the method of particular solutions with domain decomposition. We are particularly interested in asymptotic expansions of the eigenvalues \(\lambda (n)\) of shapes with n edges that are of the form \(\lambda (n) \sim x\sum _{k=0}^{\infty
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Fast numerical integration of highly oscillatory Bessel transforms with a Cauchy type singular point and exotic oscillators Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-02 Hongchao Kang, Qi Xu, Guidong Liu
In this article, we propose an efficient hybrid method to calculate the highly oscillatory Bessel integral \(\int _{0}^{1} \frac{f(x)}{x-\tau } J_{m} (\omega x^{\gamma } )\textrm{d}x\) with the Cauchy type singular point, where \( 0< \tau < 1, m \ge 0, 2\gamma \in N^{+}. \) The hybrid method is established by combining the complex integration method with the Clenshaw– Curtis– Filon– type method. Based
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Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-30 Julio Enrique Castrillón-Candás