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A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-18 Xiaojuan Liu, Maojun Li, Tao Yin, Shangyou Zhang
This paper studies the finite element method for solving the exterior Stokes problem in two dimensions. A nonlocal boundary condition is defined using a nonsingular-kernel Dirichlet-to-Dirichlet (DtD) mapping, which maps the Dirichlet data on an interior circle to the Dirichlet data on another circular artificial boundary based on the Poisson integral formula of the Stokes problem. The truncated problem
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Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-17 Ben S. Ashby, Tristan Pryer
In this article, we present a numerical method for the Stokes flow of an Oldroyd-B fluid. The viscoelastic stress evolves according to a constitutive law formulated in terms of the upper convected time derivative. A finite difference method is used to discretise along fluid trajectories to approximate the advection and deformation terms of the upper convected derivative in a simple, cheap and cohesive
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A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-13 Jan Giesselmann, Kiwoong Kwon
We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional in the sense that an a posteriori computable quantity needs to be small enough—which can be ensured by mesh refinement—and optimal in the sense that the error estimator decays with the same order as the error under mesh
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Conley Index for Multivalued Maps on Finite Topological Spaces Found. Comput. Math. (IF 2.5) Pub Date : 2024-12-09 Jonathan Barmak, Marian Mrozek, Thomas Wanner
We develop Conley’s theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we establish the notions of isolated invariant sets and index pairs, and use them to introduce a well-defined Conley index. In addition, we verify some of its fundamental properties
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Generalized Pseudospectral Shattering and Inverse-Free Matrix Pencil Diagonalization Found. Comput. Math. (IF 2.5) Pub Date : 2024-12-09 James Demmel, Ioana Dumitriu, Ryan Schneider
We present a randomized, inverse-free algorithm for producing an approximate diagonalization of any \(n \times n\) matrix pencil (A, B). The bulk of the algorithm rests on a randomized divide-and-conquer eigensolver for the generalized eigenvalue problem originally proposed by Ballard, Demmel and Dumitriu (Technical Report 2010). We demonstrate that this divide-and-conquer approach can be formulated
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Analysis of a time filtered finite element method for the unsteady inductionless MHD equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-09 Xiaodi Zhang, Jialin Xie, Xianzhu Li
This paper studies a time filtered finite element method for the unsteady inductionless magnetohydrodynamic (MHD) equations. The method uses the semi-implicit backward Euler scheme with a time filter in time and adopts the standard inf-sup stable fluid pairs to discretize the velocity and pressure, and the inf-sup stable face-volume elements for solving the current density and electric potential in
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Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-09 Khalil A. Hall-Hooper, Arvind K. Saibaba, Julianne Chung, Scot M. Miller
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for small problems but are not computationally feasible for problems with a very large number of unknown inverse parameters. In this work, we describe an empirical Bayes
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On the recovery of initial status for linearized shallow-water wave equation by data assimilation with error analysis Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-05 Jun-Liang Fu, Jijun Liu
We recover the initial status of an evolution system governed by linearized shallow-water wave equations in a 2-dimensional bounded domain by data assimilation technique, with the aim of determining the initial wave height from the measurement of wave distribution in an interior domain. Since we specify only one component of the solution to the governed system and the observation is only measured in
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Locally-Verifiable Sufficient Conditions for Exactness of the Hierarchical B-spline Discrete de Rham Complex in $$\mathbb {R}^n$$ Found. Comput. Math. (IF 2.5) Pub Date : 2024-12-04 Kendrick Shepherd, Deepesh Toshniwal
Given a domain \(\Omega \subset \mathbb {R}^n\), the de Rham complex of differential forms arises naturally in the study of problems in electromagnetism and fluid mechanics defined on \(\Omega \), and its discretization helps build stable numerical methods for such problems. For constructing such stable methods, one critical requirement is ensuring that the discrete subcomplex is cohomologically equivalent
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Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-04 Maya Briani, Emiliano Cristiani, Elia Onofri
In this paper, we develop new methods to join machine learning techniques and macroscopic differential models, aimed at estimate and forecast vehicular traffic. This is done to complement respective advantages of data-driven and model-driven approaches. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class
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Solving the quadratic eigenvalue problem expressed in non-monomial bases by the tropical scaling Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-03 Hongjia Chen, Teng Wang, Chun-Hua Zhang, Xiang Wang
In this paper, we consider the quadratic eigenvalue problem (QEP) expressed in various commonly used bases, including Taylor, Newton, and Lagrange bases. We propose to investigate the backward errors of the computed eigenpairs and condition numbers of eigenvalues for QEP solved by a class of block Kronecker linearizations. To improve the backward error and condition number of the QEP expressed in a
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Constrained and Unconstrained Stable Discrete Minimizations for p-Robust Local Reconstructions in Vertex Patches in the de Rham Complex Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-25 Théophile Chaumont-Frelet, Martin Vohralík
We analyze constrained and unconstrained minimization problems on patches of tetrahedra sharing a common vertex with discontinuous piecewise polynomial data of degree p. We show that the discrete minimizers in the spaces of piecewise polynomials of degree p conforming in the \(H^1\), \({\varvec{H}}(\textbf{curl})\), or \({\varvec{H}}({\text {div}})\) spaces are as good as the minimizers in these entire
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Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis Adv. Comput. Math. (IF 1.7) Pub Date : 2024-11-25 J.K. Djoko, T. Sayah
In two dimensions, we propose and analyse an iterative a posteriori error indicator for the discontinuous Galerkin finite element approximations of the Stokes equations under boundary conditions of friction type. Two sources of error are identified here, namely; the discretisation error and the linearization error. Under a smallness assumption on data, we prove that the devised error estimator is reliable
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Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-20 Brendan Keith, Thomas M. Surowiec
The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent
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Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies Adv. Comput. Math. (IF 1.7) Pub Date : 2024-11-18 M. Averseng, J. Galkowski, E. A. Spence
For h-FEM discretisations of the Helmholtz equation with wavenumber k, we obtain k-explicit analogues of the classic local FEM error bounds of Nitsche and Schatz (Math. Comput. 28(128), 937–958 1974), Wahlbin (1991, §9), Demlow et al.(Math. Comput. 80(273), 1–9 2011), showing that these bounds hold with constants independent of k, provided one works in Sobolev norms weighted with k in the natural way
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Higher-order iterative decoupling for poroelasticity Adv. Comput. Math. (IF 1.7) Pub Date : 2024-11-15 Robert Altmann, Abdullah Mujahid, Benjamin Unger
For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As the main result, we show that the convergence depends on the interplay between
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Classification of Finite Groups: Recent Developements and Open Problems Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-12 Bettina Eick
The theory of group classifications has undergone significant changes in the past 25 years. New methods have been introduced, some difficult problems have been solved and group classifications have become widely available through computer algebra systems. This survey describes the state of the art of the group classification problem, its history, its recent advances and some open problems.
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Computing the Noncommutative Inner Rank by Means of Operator-Valued Free Probability Theory Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-11 Johannes Hoffmann, Tobias Mai, Roland Speicher
We address the noncommutative version of the Edmonds’ problem, which asks to determine the inner rank of a matrix in noncommuting variables. We provide an algorithm for the calculation of this inner rank by relating the problem with the distribution of a basic object in free probability theory, namely operator-valued semicircular elements. We have to solve a matrix-valued quadratic equation, for which
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Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-11 Sadashige Ishida, Hugo Lavenant
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also
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Gabor Phase Retrieval via Semidefinite Programming Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-07 Philippe Jaming, Martin Rathmair
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Anita T. Layton
SIAM Review, Volume 66, Issue 4, Page 795-805, November 2024. If you are teaching a course (or otherwise looking for a text) in the techniques and applications of mathematical modeling, or mathematical approaches that analyze or solve those equations, you may find one of the reviews in this issue's collection interesting. Our featured review was written by Shawn Ryan, on the book Mathematical Modeling
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Developing Workforce with Mathematical Modeling Skills SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Ariel Cintrón-Arias, Ryan Andrew Nivens, Anant Godbole, Calvin B. Purvis
SIAM Review, Volume 66, Issue 4, Page 778-792, November 2024. Mathematicians have traditionally been a select group of academics who produce high-impact ideas enabling substantial results in several fields of science. Throughout the past 35 years, undergraduates enrolling in mathematics or statistics have represented a nearly constant proportion of approximately 1% of bachelor degrees awarded in the
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Sandpiles and Dunes: Mathematical Models for Granular Matter SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Piermarco Cannarsa, Stefano Finzi Vita
SIAM Review, Volume 66, Issue 4, Page 751-777, November 2024. Granular materials are everywhere, in the environment but also in our pantry. Their properties are different from those of any solid material, due to the possibility of sudden phenomena such as avalanches or landslides. Here we present a brief survey on their characteristics and on what can be found (from the past thirty years) in the recent
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Education SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Hélène Frankowska
SIAM Review, Volume 66, Issue 4, Page 749-749, November 2024. In this issue the Education section presents two contributions. The first paper, “Sandpiles and Dunes: Mathematical Models for Granular Matter,” by Piermarco Cannarsa and Stefano Finzi Vita, presents a review of mathematical models for formation of sand piles and dunes. In nature and everyday life various materials appear as conglomerates
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A Bridge between Invariant Theory and Maximum Likelihood Estimation SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal
SIAM Review, Volume 66, Issue 4, Page 721-747, November 2024. We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We present a dictionary that relates notions of stability from geometric invariant theory to the existence and uniqueness of a maximum likelihood estimate. Our dictionary holds for both discrete and continuous
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SIGEST SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 The Editors
SIAM Review, Volume 66, Issue 4, Page 719-719, November 2024. The SIGEST article in this issue, “A Bridge between Invariant Theory and Maximum Likelihood Estimation,” by Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, and Anna Seigal, uncovers the deep connections between geometric invariant theory and statistical methods, specifically maximum likelihood estimation (MLE) by connecting it to norm
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Feynman's Inverse Problem SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Adrian Kirkeby
SIAM Review, Volume 66, Issue 4, Page 694-718, November 2024. We analyze an inverse problem for water waves posed by Richard Feynman in the BBC documentary Fun to Imagine. We show that the problem can be modeled as an inverse Cauchy problem for gravity-capillary waves, conduct a detailed analysis of the Cauchy problem, and give a uniqueness proof for the inverse problem. Somewhat surprisingly, this
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Sigmoid Functions, Multiscale Resolution of Singularities, and $hp$-Mesh Refinement SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Daan Huybrechs, Lloyd N. Trefethen
SIAM Review, Volume 66, Issue 4, Page 683-693, November 2024. In this short, conceptual paper we observe that closely related mathematics applies in four contexts with disparate literatures: (1) sigmoidal and RBF approximation of smooth functions, (2) rational approximation of analytic functions with singularities, (3) $hp\kern .7pt$-mesh refinement for solution of \pdes, and (4) double exponential
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Research Spotlights SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Stefan M. Wild
SIAM Review, Volume 66, Issue 4, Page 681-681, November 2024. Logarithmic transformations are used broadly in data science, mathematics, and engineering, and yet they can still reveal surprising connections between seemingly unrelated disciplines. This issue's first research spotlight, “Sigmoid Functions, Multiscale Resolution of Singularities, and $hp$-Mesh Refinement,” illuminates how the change
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Oscillatory Networks: Insights from Piecewise-Linear Modeling SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Stephen Coombes, Mustafa Şayli, Rüdiger Thul, Rachel Nicks, Mason A. Porter, Yi Ming Lai
SIAM Review, Volume 66, Issue 4, Page 619-679, November 2024. There is enormous interest---both mathematically and in diverse applications---in understanding the dynamics of coupled-oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology, and more. It is common to describe the rich emergent behavior in these systems in terms of complex patterns
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Survey and Review SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Marlis Hochbruck
SIAM Review, Volume 66, Issue 4, Page 617-617, November 2024. Neural oscillations are periodic activities of neurons in the central nervous system of eumetazoa. In an oscillatory neural network, neurons are modeled by coupled oscillators. Oscillatory networks are employed for describing the behavior of complex systems in biology or ecology with respect to the connectivity of the network components
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A Theory of the NEPv Approach for Optimization on the Stiefel Manifold Found. Comput. Math. (IF 2.5) Pub Date : 2024-10-31 Ren-Cang Li
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Adaptive quarklet tree approximation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-31 Stephan Dahlke, Marc Hovemann, Thorsten Raasch, Dorian Vogel
This paper is concerned with near-optimal approximation of a given univariate function with elements of a polynomially enriched wavelet frame, a so-called quarklet frame. Inspired by hp-approximation techniques of Binev, we use the underlying tree structure of the frame elements to derive an adaptive algorithm that, under standard assumptions concerning the local errors, can be used to create approximations
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Efficient computation of the sinc matrix function for the integration of second-order differential equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-28 Lidia Aceto, Fabio Durastante
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Sobolev regularity of bivariate isogeometric finite element spaces in case of a geometry map with degenerate corner Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-24 Ulrich Reif
We investigate Sobolev regularity of bivariate functions obtained in Isogeometric Analysis when using geometry maps that are degenerate in the sense that the first partial derivatives vanish at isolated points. In particular, we show how the known \(C^1\)-conditions for D-patches have to be tightened to guarantee square integrability of second partial derivatives, as required when computing finite
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An optimal ansatz space for moving least squares approximation on spheres Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-22 Ralf Hielscher, Tim Pöschl
We revisit the moving least squares (MLS) approximation scheme on the sphere \(\mathbb S^{d-1} \subset {\mathbb R}^d\), where \(d>1\). It is well known that using the spherical harmonics up to degree \(L \in {\mathbb N}\) as ansatz space yields for functions in \(\mathcal {C}^{L+1}(\mathbb S^{d-1})\) the approximation order \(\mathcal {O}\left( h^{L+1} \right) \), where h denotes the fill distance
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A unified local projection-based stabilized virtual element method for the coupled Stokes-Darcy problem Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-21 Sudheer Mishra, E. Natarajan
In this work, we propose and analyze a new stabilized virtual element method for the coupled Stokes-Darcy problem with Beavers-Joseph-Saffman interface condition on polygonal meshes. We derive two variants of local projection stabilization methods for the coupled Stokes-Darcy problem. The significance of local projection-based stabilization terms is that they provide reasonable control of the pressure
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Explicit A Posteriori Error Representation for Variational Problems and Application to TV-Minimization Found. Comput. Math. (IF 2.5) Pub Date : 2024-10-18 Sören Bartels, Alex Kaltenbach
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A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-14 Huoyuan Duan, Roger C. E. Tan, Duowei Zhu
With local pressure-residual stabilizations as an augmentation to the classical Galerkin/least-squares (GLS) stabilized method, a new locally evaluated residual-based stabilized finite element method is proposed for a type of Stokes equations from the incompressible flows. We focus on the study of a type of nonstandard boundary conditions involving the mixed tangential velocity and pressure Dirichlet
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A stochastic perturbation analysis of the QR decomposition and its applications Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-02 Tianru Wang, Yimin Wei
The perturbation of the QR decompostion is analyzed from the probalistic point of view. The perturbation error is approximated by a first-order perturbation expansion with high probability where the perturbation is assumed to be random. Different from the previous normwise perturbation bounds using the Frobenius norm, our techniques are used to develop the spectral norm, as well as the entry-wise perturbation
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An electrical engineering perspective on naturality in computational physics Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-01 P. Robert Kotiuga, Valtteri Lahtinen
We look at computational physics from an electrical engineering perspective and suggest that several concepts of mathematics, not so well-established in computational physics literature, present themselves as opportunities in the field. We discuss elliptic complexes and highlight the category theoretical background and its role as a unifying language between algebraic topology, differential geometry
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The Gromov–Wasserstein Distance Between Spheres Found. Comput. Math. (IF 2.5) Pub Date : 2024-09-16 Shreya Arya, Arnab Auddy, Ranthony A. Clark, Sunhyuk Lim, Facundo Mémoli, Daniel Packer
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Unbiasing Hamiltonian Monte Carlo Algorithms for a General Hamiltonian Function Found. Comput. Math. (IF 2.5) Pub Date : 2024-09-16 T. Lelièvre, R. Santet, G. Stoltz
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Maximal volume matrix cross approximation for image compression and least squares solution Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-16 Kenneth Allen, Ming-Jun Lai, Zhaiming Shen
We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume submatrices. More precisely, we present a new proof of the classic estimate of the inequality with an improved constant. Also, we present a family of greedy maximal
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Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-14 Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner, Christoph Schwab
The distribution of centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds is determined by their covariance operators. We consider centered GRFs given as variational solutions to coloring operator equations driven by spatial white noise, with an elliptic self-adjoint pseudodifferential coloring operator from
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Improved a posteriori error bounds for reduced port-Hamiltonian systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-11 Johannes Rettberg, Dominik Wittwar, Patrick Buchfink, Robin Herkert, Jörg Fehr, Bernard Haasdonk
Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a) a hierarchical
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Interpolating refinable functions and $$n_s$$ -step interpolatory subdivision schemes Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-05 Bin Han
Standard interpolatory subdivision schemes and their underlying interpolating refinable functions are of interest in CAGD, numerical PDEs, and approximation theory. Generalizing these notions, we introduce and study \(n_s\)-step interpolatory \(\textsf{M}\)-subdivision schemes and their interpolating \(\textsf{M}\)-refinable functions with \(n_s\in \mathbb {N}\cup \{\infty \}\) and a dilation factor
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SVD-based algorithms for tensor wheel decomposition Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-05 Mengyu Wang, Honghua Cui, Hanyu Li
Tensor wheel (TW) decomposition combines the popular tensor ring and fully connected tensor network decompositions and has achieved excellent performance in tensor completion problem. A standard method to compute this decomposition is the alternating least squares (ALS). However, it usually suffers from slow convergence and numerical instability. In this work, the fast and robust SVD-based algorithms
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Signed Barcodes for Multi-parameter Persistence via Rank Decompositions and Rank-Exact Resolutions Found. Comput. Math. (IF 2.5) Pub Date : 2024-09-04 Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot
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Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-02 Desong Kong, Jie Shen, Li-Lian Wang, Shuhuang Xiang
In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulting from the Legendre dual-Petrov-Galerkin (LDPG) method for the mth-order initial value problem (IVP): \(u^{(m)}(t)=\sigma u(t),\, t\in (-1,1)\) with constant \(\sigma \not =0\) and usual initial conditions at t\(=-1,\) are associated with the generalised Bessel polynomials (GBPs). In particular
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On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-28 Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni, Paolo Zunino
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Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-27 Dirk Pauly, Rainer Picard
In this short note we show that Hilbert complexes are strongly related to what we shall call annihilating sets of skew-selfadjoint operators. This provides for a new perspective on the classical topic of Hilbert complexes viewed as families of commuting normal operators.
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New Ramsey Multiplicity Bounds and Search Heuristics Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-26 Olaf Parczyk, Sebastian Pokutta, Christoph Spiegel, Tibor Szabó
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Grounded Persistent Path Homology: A Stable, Topological Descriptor for Weighted Digraphs Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-23 Thomas Chaplin, Heather A. Harrington, Ulrike Tillmann
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Learning Time-Scales in Two-Layers Neural Networks Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-22 Raphaël Berthier, Andrea Montanari, Kangjie Zhou
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Computing eigenvalues of quasi-rational Said–Ball–Vandermonde matrices Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-22 Xiaoxiao Ma, Yingqing Xiao
This paper focuses on computing the eigenvalues of the generalized collocation matrix of the rational Said–Ball basis, also called as the quasi-rational Said–Ball–Vandermonde (q-RSBV) matrix, with high relative accuracy. To achieve this, we propose explicit expressions for the minors of the q-RSBV matrix and develop a high-precision algorithm to compute these parameters. Additionally, we present perturbation
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Morley type virtual element method for von Kármán equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-22 Devika Shylaja, Sarvesh Kumar
This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von Kármán equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error
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Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-19 Bernard Kapidani, Melina Merkel, Sebastian Schöps, Rafael Vázquez
Common formulations of the eddy current problem involve either vector or scalar potentials, each with its own advantages and disadvantages. An impasse arises when using scalar potential-based formulations in the presence of conductors with non-trivial topology. A remedy is to augment the approximation spaces with generators of the first cohomology group. Most existing algorithms for this require a
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The Universal Equivariance Properties of Exotic Aromatic B-Series Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-16 Adrien Laurent, Hans Munthe-Kaas