Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices: Multifidelity covariance estimation via regression on the manifold of symmetric positive definite matrices

Authors: Aimee Maurais, Terrence Alsup, Benjamin Peherstorfer, Youssef M. Marzouk

Source: SIAM Journal on Mathematics of Data Science. 7:189-223

Subject Terms: FOS: Computer and information sciences, covariance estimation, Computer Science - Machine Learning, Numerical solutions of ill-posed problems in abstract spaces, regularization, Numerical solutions to equations with nonlinear operators, multifidelity methods, Numerical Analysis (math.NA), estimation on manifolds, Statistics - Computation, Machine Learning (cs.LG), Positive matrices and their generalizations, cones of matrices, Numerical solutions to equations with linear operators, Special polytopes (linear programming, centrally symmetric, etc.), General nonlinear regression, FOS: Mathematics, Mathematics - Numerical Analysis, Riemannian geometry, Mahalanobis distance, Statistics on manifolds, Computation (stat.CO), statistical coupling

File Description: application/xml

Access URL: http://arxiv.org/abs/2307.12438

An accurate coupled method for analysis of transcranial magneto-acoustic-electrical stimulation

Authors: Wang, Z. H., Shang, K., Wang, G.

Source: Applied Mathematical Modelling. 128:470-491

Subject Terms: Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory, transcranial magneto-acoustic-electrical stimulation, Numerical solutions to equations with linear operators, numerical methods, Rayleigh integral, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, magneto-acoustic coupling, smoothed finite element method

File Description: application/xml

Access URL: https://zbmath.org/7996749
https://doi.org/10.1016/j.apm.2024.01.023

Solution of linear ill-posed operator equations by modified truncated singular value expansion

Authors: Laura Dykes, Mykhailo Kuian, Thomas Mach, Silvia Noschese, Lothar Reichel

Source: Journal of Computational and Applied Mathematics. 467:116621

Subject Terms: regularization, truncated singular value expansion, Numerical solutions of ill-posed problems in abstract spaces, Linear operators and ill-posed problems, regularization, Numerical solutions to equations with linear operators, ill-posed problem, Chebfun

File Description: application/xml; application/pdf

Symmetric-conjugate splitting methods for evolution equations of parabolic type

Authors: Blanes Zamora, Sergio, Casas, F., González, C., Thalhammer, M.

Contributors: Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial, Instituto Universitario de Matemática Multidisciplinar, Generalitat Valenciana, Agencia Estatal de Investigación, Repositorio Institucional de la Universitat Politècnica de València Riunet

Source: RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Universitat Politècnica de València (UPV)

Subject Terms: Abstract parabolic equations, Fourier spectral methods, 65J10, 65L04, 65M12, convergence, Schrodinger equations, Linear evolution equations, Efficiency, Schrödinger equations, stability, linear evolution equations, Linear differential equations in abstract spaces, efficiency, Numerical solutions to equations with linear operators, Numerical methods for stiff equations, Operator splitting methods, Parabolic problems, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Convergence, MATEMATICA APLICADA, parabolic problems, operator splitting methods, Stability, Physics - Computational Physics

File Description: application/pdf; application/xml

Access URL: http://arxiv.org/abs/2401.04196
https://riunet.upv.es/handle/10251/206519

Tensor-product split-simplex summation-by-parts operators

Authors: Zelalem Arega Worku, Jason E. Hicken, David W. Zingg

Source: Journal of Computational Physics. 527:113796

Subject Terms: tensor-product operator, summation-by-parts, Numerical solutions to equations with linear operators, high-order method, Multilinear algebra, tensor calculus, unstructured mesh, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, simplex

File Description: application/xml

Access URL: http://arxiv.org/abs/2408.10494
https://zbmath.org/8021096
https://doi.org/10.1016/j.jcp.2025.113796

An efficient Galerkin method for problems with physically realistic boundary conditions

Authors: Podvigina, Olga

Source: Computer Physics Communications. 309:109482

Subject Terms: Numerical solutions to equations with linear operators, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Galerkin, boundary condition

File Description: application/xml

Access URL: http://arxiv.org/abs/2312.15337

Discrete maximal regularity and the finite element method for parabolic equations

Authors: Tomoya Kemmochi, Norikazu Saito

Source: Numerische Mathematik. 138:905-937

Subject Terms: regularity, Smoothness and regularity of solutions to PDEs, finite element method, parabolic equations, Numerical Analysis (math.NA), semilinear heat equations, Error bounds for initial value and initial-boundary value problems involving PDEs, Numerical solutions to equations with linear operators, 35K91, 65M60, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: http://arxiv.org/pdf/1602.06864
http://arxiv.org/abs/1602.06864
https://zbmath.org/6858661
https://doi.org/10.1007/s00211-017-0929-z
https://dblp.uni-trier.de/db/journals/nm/nm138.html#KemmochiS18
https://link.springer.com/article/10.1007/s00211-017-0929-z

Randomized dynamic mode decomposition for nonintrusive reduced order modelling

Authors: Diana Alina Bistrian, Ionel Michael Navon

Source: International Journal for Numerical Methods in Engineering. 112:3-25

Subject Terms: 65P99, 76B75, nonintrusive reduced order modelling, randomized SVD, Numerical solutions to equations with linear operators, Navier-Stokes equations for incompressible viscous fluids, 0103 physical sciences, FOS: Mathematics, randomized dynamic mode decomposition, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: http://arxiv.org/pdf/1611.04884
http://arxiv.org/abs/1611.04884
https://zbmath.org/7867129
https://doi.org/10.1002/nme.5499
https://ui.adsabs.harvard.edu/abs/2017IJNME.112....3B/abstract
https://onlinelibrary.wiley.com/doi/10.1002/nme.5499

Runge–Kutta integrators yield optimal regularization schemes: Runge-Kutta integrators yield optimal regularization schemes

Authors: Rieder, A.

Source: Inverse Problems, 21 (2), 453-471

Subject Terms: ddc:510, numerical examples, convergence, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Showalter's method, Tikhonov regularization, Hilbert space, asymptotic regularization, implicit Euler scheme, 01 natural sciences, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Linear differential equations in abstract spaces, Numerical solutions to equations with linear operators, evolution equation, linear ill-posed problems, 0101 mathematics, Runge-Kutta integrators, order optimality, Mathematics

File Description: application/xml; application/pdf

Access URL: https://publikationen.bibliothek.kit.edu/1000011042/762671
https://zbmath.org/2174678
https://doi.org/10.1088/0266-5611/21/2/003
http://digbib.ubka.uni-karlsruhe.de/volltexte/documents/762671
http://ui.adsabs.harvard.edu/abs/2005InvPr..21..453R/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/21/2/003
http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-110850
https://publikationen.bibliothek.kit.edu/1000011085/772258
https://doi.org/10.5445/IR/1000011085
https://publikationen.bibliothek.kit.edu/1000011085
http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-110428
https://doi.org/10.5445/IR/1000011042
https://publikationen.bibliothek.kit.edu/1000011042
https://publikationen.bibliothek.kit.edu/1000011042/762671

Adaptive Wavelet Galerkin Methods for Linear Inverse Problems: Adaptive wavelet Galerkin methods for linear inverse problems

Authors: Cohen, Albert, Hoffmann, Marc, Reiß, Markus

Source: SIAM Journal on Numerical Analysis. 42:1479-1501

Subject Terms: nonlinear methods, ddc:330, 330 Wirtschaft, Numerical solution to inverse problems in abstract spaces, Numerical methods for integral equations, wavelets, 01 natural sciences, Galerkin methods, numerical example, Numerical solutions to equations with linear operators, Besov spaces, Numerical methods for wavelets, statistical inverse problems, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), 0101 mathematics, minimax estimation, singular integral equation, Equations and inequalities involving linear operators, with vector unknowns

File Description: application/xml; application/pdf

Access URL: https://edoc.hu-berlin.de/bitstream/18452/4148/1/50.pdf
https://zbmath.org/2139932
https://doi.org/10.1137/s0036142902411793
http://hdl.handle.net/10419/65296
https://www.econstor.eu/bitstream/10419/65296/1/726723541.pdf

On the rate of convergence of the alternating projection method in finite dimensional spaces

Authors: Aurél Galántai

Source: Journal of Mathematical Analysis and Applications. 310:30-44

Subject Terms: alternating projection method, orthogonal projections, Numerical solutions to equations with linear operators, Applied Mathematics, Numerical linear algebra, Rate of convergence, degree of approximation, 0101 mathematics, 01 natural sciences, Analysis, rate of convergence

File Description: application/xml

Access URL: https://zbmath.org/2207251
https://doi.org/10.1016/j.jmaa.2004.12.050
https://core.ac.uk/display/81979253
https://www.sciencedirect.com/science/article/pii/S0022247X04010716
https://ui.adsabs.harvard.edu/abs/2005JMAA..310...30G/abstract

A new discrepancy principle

Authors: Alexander G. Ramm

Source: Journal of Mathematical Analysis and Applications. 310:342-345

Subject Terms: 47H15, 45G10,35B25, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Applied Mathematics, discrepancy principle, Hilbert space, Numerical Analysis (math.NA), minimal-norm solution, 01 natural sciences, ill-posed problems, Numerical solutions to equations with linear operators, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Analysis

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0408191
https://zbmath.org/2207275
https://doi.org/10.1016/j.jmaa.2005.01.062
https://core.ac.uk/display/21861235
https://arxiv.org/pdf/math/0408191
https://www.sciencedirect.com/science/article/pii/S0022247X05000910
https://www.math.ksu.edu/~ramm/papers/480j.pdf
http://www.math.ksu.edu/~ramm/papers/480j.pdf
http://ui.adsabs.harvard.edu/abs/2005JMAA..310..342R/abstract

Preconditioning Landweber iteration in Hilbert scales

Authors: Herbert Egger, Andreas Neubauer

Source: Numerische Mathematik. 101:643-662

Subject Terms: Landweber iteration, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, preconditioning, Numerical solutions to equations with nonlinear operators, Numerical solutions to equations with linear operators, Nonlinear ill-posed problems, Numerical solution to inverse problems in abstract spaces, numerical results, 0101 mathematics, ill-posed inverse problems, Hilbert scales, 01 natural sciences

File Description: application/xml

On a quasi-optimal regularized projection method for solving operator equations of the first kind

Authors: S. G. Solodky

Source: Inverse Problems. 21:1473-1485

Subject Terms: Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Hilbert space, discrepancy principle, ill-posed problem, Showalter method, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, Tikhonov method, regularization methods, compact linear operator, Numerical solutions to equations with linear operators, optimal order of accuracy, 0101 mathematics, linear operator equation, regularized projection method algorithm

File Description: application/xml

Access URL: https://zbmath.org/2215125
https://doi.org/10.1088/0266-5611/21/4/017
https://ui.adsabs.harvard.edu/abs/2005InvPr..21.1473S/abstract
http://iopscience.iop.org/article/10.1088/0266-5611/21/4/017/pdf

Regularization of ill-posed problems in Banach spaces: convergence rates

Authors: Elena Resmerita

Source: Inverse Problems. 21:1303-1314

Subject Terms: ill-posed problems, regularization, linear bounded compact operator, convergence, Numerical solutions of ill-posed problems in abstract spaces, Linear operators and ill-posed problems, regularization, Numerical solutions to equations with linear operators, Hilbert space, 0101 mathematics, 01 natural sciences, Bregman distance, entropic regularization, total variation regularization

File Description: application/xml

Access URL: https://ui.adsabs.harvard.edu/abs/2005InvPr..21.1303R/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/21/4/007/meta

Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations

Authors: Becker, Roland, Vexler, Boris

Contributors: Becker, Roland

Source: Journal of Computational Physics. 206:95-110

Subject Terms: Hilbert spaces, Variational methods for second-order elliptic equations, error estimator, Error bounds for boundary value problems involving PDEs, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, 01 natural sciences, least squares, discretizaton errors, sensitivity analysis, Numerical solutions to equations with linear operators, Parameter estimation, adaptive mesh refinement, 0101 mathematics, parameter estimation, Galerkin method, measurement errors, Equations and inequalities involving linear operators, with vector unknowns

File Description: application/xml; application/pdf

Access URL: http://www.ricam.oeaw.ac.at/publications/reports/04/rep04-15.pdf
https://zbmath.org/2175561
https://doi.org/10.1016/j.jcp.2004.12.018
https://hal.science/hal-00158887v1
https://hal.inria.fr/hal-00158887
https://hal.archives-ouvertes.fr/hal-00158887/document
https://hal.archives-ouvertes.fr/hal-00158887
https://memsic.ccsd.cnrs.fr/UNIV-PAU/hal-00158887
http://www.ricam.oeaw.ac.at/publications/reports/04/rep04-15.pdf
http://www.sciencedirect.com/science/article/pii/S0021999104004954

A note on the second order of accuracy difference schemes for hyperbolic–parabolic equations: A note on the second order of accuracy difference schemes for hyperbolic--parabolic equations

Authors: Allaberen Ashyralyev, H. A. Yurtsever

Source: Applied Mathematics and Computation. 165:517-537

Subject Terms: nonlocal boundary value problem, PDEs of mixed type, Hilbert space, 01 natural sciences, hyperbolic-parabolic equation, Linear differential equations in abstract spaces, Error bounds for initial value and initial-boundary value problems involving PDEs, stability estimates, Numerical solutions to equations with linear operators, Finite difference methods for initial value and initial-boundary value problems involving PDEs, self-adjoint positive definite operator, mixed type boundary value problem, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, numerical experiments, second order of accuracy difference schemes

File Description: application/xml

Access URL: https://zbmath.org/2175470
https://doi.org/10.1016/j.amc.2004.04.033
https://www.sciencedirect.com/science/article/pii/S0096300304003996
https://dblp.uni-trier.de/db/journals/amc/amc165.html#AshyralyevY05

Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems

Authors: Freitag, Melina A, Hofmann, B

Source: Freitag, M A & Hofmann, B 2005, 'Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems', Journal of Inverse and Ill-posed Problems, vol. 13, no. 2, pp. 123-148. https://doi.org/10.1515/1569394053978524

Subject Terms: Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, Tikhonov regularization, name=Applied Mathematics, Numerical solution to inverse problems in abstract spaces, compact operator, ill-posed problem, multiplication operators, 01 natural sciences, Nemytskij operator, linear operator equations, Numerical solutions to equations with linear operators, 0101 mathematics

File Description: application/xml; application/pdf

Access URL: https://purehost.bath.ac.uk/ws/files/141101243/endversion.pdf
https://zbmath.org/2204565
https://doi.org/10.1515/1569394053978524
https://purehost.bath.ac.uk/ws/files/141101243/endversion.pdf
https://researchportal.bath.ac.uk/en/publications/analytical-and-numerical-studies-on-the-influence-of-multiplicati
https://core.ac.uk/display/2810776

Convergence rates for Tikhonov regularization based on range inclusions

Authors: Bernd Hofmann, Masahiro Yamamoto

Source: Inverse Problems. 21:805-820

Subject Terms: Hilbert spaces, Inverse problems for PDEs, Tikhonov's regularization method, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs, Numerical methods for integral equations, 01 natural sciences, Abel integral equation, Numerical solutions to equations with linear operators, linear ill-posed problems, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), 0101 mathematics

File Description: application/xml

Access URL: https://www.tu-chemnitz.de/mathematik/inverse_probleme/fulltext/inclusion.pdf
https://ui.adsabs.harvard.edu/abs/2005InvPr..21..805H/abstract

B-splines and discretization in an inverse problem for Poisson processes

Authors: Zbigniew Szkutnik

Source: Journal of Multivariate Analysis. 93:198-221

Subject Terms: Statistics and Probability, Numerical Analysis, Computational problems in statistics, Quasi-maximum likelihood estimators, Monte Carlo methods, Poisson process, Unfolding, Non-Markovian processes: estimation, 01 natural sciences, Numerical computation using splines, Asymptotic properties of nonparametric inference, Numerical solutions to equations with linear operators, B-spline sieves, Intensity function, Statistics, Probability and Uncertainty, 0101 mathematics, Nonparametric estimation, Discretization

File Description: application/xml

Access URL: https://zbmath.org/2132937
https://doi.org/10.1016/j.jmva.2004.01.008
https://core.ac.uk/display/81154539
https://dl.acm.org/doi/10.1016/j.jmva.2004.01.008
https://econpapers.repec.org/RePEc:eee:jmvana:v:93:y:2005:i:1:p:198-221
https://www.sciencedirect.com/science/article/pii/S0047259X0400020X
https://ideas.repec.org/a/eee/jmvana/v93y2005i1p198-221.html