Search Results - "Ill-posedness and regularization problems in numerical linear algebra"

A Preconditioned Version of a Nested Primal-Dual Algorithm for Image Deblurring: A preconditioned version of a nested primal-dual algorithm for image deblurring

Authors: Stefano Aleotti Marco Donatelli Rolf Krause et al.

Source: Journal of Scientific Computing. 103

Subject Terms: ill-posed problems, Numerical optimization and variational techniques, convex optimization, Ill-posedness and regularization problems in numerical linear algebra, preconditioning, Numerical aspects of computer graphics, image analysis, and computational geometry, FOS: Mathematics, 65F22 (Primary) 65K10 (Secondary), Mathematics - Numerical Analysis, Numerical Analysis (math.NA), image deblurring

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Access URL: http://arxiv.org/abs/2409.13454

A method for solving ill-conditioned separable nonlinear least squares problems and its application

Authors: Wang, Luyao Liu, Guolin Chen, Yang et al.

Source: Journal of Computational and Applied Mathematics. 466:116624

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, variable projection, Ill-posedness and regularization problems in numerical linear algebra, ridge estimation, singular value decomposition, Orthogonalization in numerical linear algebra, ill-conditioned matrix, height anomaly

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Access URL: https://zbmath.org/8031358
https://doi.org/10.1016/j.cam.2025.116624

Retrieval of initial condition for Burgers' equation using reduced-order EnKF via POD-based sparse observations

Authors: Li, Jie Wang, Yuepeng Ren, Zhigang

Source: Journal of Industrial and Management Optimization. 19:4222-4232

Subject Terms: Ill-posedness and regularization problems in numerical linear algebra, KdV equations (Korteweg-de Vries equations), Burgers' equation, data assimilation, QD algorithm, sparse observations, ensemble Kalman filter, Inference from stochastic processes and prediction

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The asymptotic distribution of the condition number for random circulant matrices

Authors: Gerardo Barrera Paulo Manrique-Mirón Department of Mathematics and Statistics

Contributors: Gerardo Barrera Paulo Manrique-Mirón Department of Mathematics and Statistics

Source: Extremes. 25:567-594

Subject Terms: Numerical computation of matrix norms, conditioning, scaling, Circulant matrix, Social Sciences, Normalization (sociology), Estimator, 01 natural sciences, POISSON STATISTICS, Random Matrix Theory and Its Applications, Decision Sciences, Independent and identically distributed random variables, Sociology, CONVERGENCE, MAXIMA, Mathematical Physics, 60F05, 60G70, 65F35, 60G10, 62E20, 65F22 62E20, 65F22, Eigenvalues and eigenvectors, Asymptotic distribution, Scaling Limits of Interacting Particle Systems, Physics, Extreme value theory, Statistics, Random matrix, Numerical Analysis (math.NA), FOS: Sociology, Random matrices (probabilistic aspects), LIMITING SPECTRAL DISTRIBUTION, NORM, Gumbel distribution, Frechet distribution, TAILS, Physical Sciences, PERIODOGRAM, Probability distributions: general theory, Mathematics - Probability, condition number, Statistics and Probability, Random variable, Management Science and Operations Research, Circulant random matrices, Mathematical analysis, Quantum mechanics, FOURIER-TRANSFORMS, SAMPLE COVARIANCE MATRICES, extremal stochastic processes, Joint probability distribution, Fréchet distribution, Stationary stochastic processes, FOS: Mathematics, Rayleigh distribution, Scaling Limits, LARGEST EIGENVALUES, Mathematics - Numerical Analysis, Condition number, 0101 mathematics, Modeling Risk in Insurance and Finance, Asymptotic distribution theory in statistics, Distribution (mathematics), Lyapunov integrability condition, Probability (math.PR), Singular value, circulant random matrices, Dimension (graph theory), Ill-posedness and regularization problems in numerical linear algebra, Combinatorics, Anthropology, Mathematics

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Access URL: http://arxiv.org/abs/2109.02282
http://hdl.handle.net/10138/350704

Sparse-regularized high-frequency enhanced neural network for solving high-frequency problems

Authors: Qilin Huang Mingjin Fang Dongsheng Cheng et al.

Source: Journal of Computational Physics. 523:113676

Subject Terms: high-frequency problem, Ill-posedness and regularization problems in numerical linear algebra, data-driven learning, partial differential equation, deep neural network, sparse learning, Spectral, collocation and related methods for boundary value problems involving PDEs, Artificial neural networks and deep learning

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Efficient sparsity-promoting MAP estimation for Bayesian linear inverse problems

Authors: Jonathan Lindbloom Jan Glaubitz Anne Gelb

Source: Inverse Problems. 41:025001

Subject Terms: Iterative numerical methods for linear systems, convexity, Beräkningsmatematik, Stochastic approximation, Bayesian inverse problems, sparsity-promoting hierarchical Bayesian learning, image reconstruction, 01 natural sciences, conditionally Gaussian priors, Computational Mathematics, Ill-posedness and regularization problems in numerical linear algebra, (generalized) gamma hyper-priors, 0101 mathematics, Stochastic matrices

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Access URL: https://zbmath.org/7976342
https://doi.org/10.1088/1361-6420/ada17f
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-211053

Joint inversion of compact operators

Authors: Jodi L. Mead James F. Ford

Source: Journal of Inverse and Ill-posed Problems. 28:105-118

Subject Terms: regularization, CGISS, Ill-posedness and regularization problems in numerical linear algebra, singular values, joint inversion, Inverse problems in geophysics, Inverse problems in linear algebra, Numerical methods for inverse problems for integral equations, 01 natural sciences, Mathematics, compact operators, 0105 earth and related environmental sciences

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Access URL: https://scholarworks.boisestate.edu/cgi/viewcontent.cgi?article=2391&context=td

Estimating Qsvt Angles for Matrix Inversion with Large Condition Numbers: Estimating QSVT angles for matrix inversion with large condition numbers

Authors: I. Novikau I. Joseph

Source: Journal of Computational Physics. 525:113767

Subject Terms: QSVT, Quantum Physics, Ill-posedness and regularization problems in numerical linear algebra, Numerical methods for low-rank matrix approximation, matrix compression, FOS: Physical sciences, quantum linear system algorithm, Computational Physics (physics.comp-ph), Quantum Physics (quant-ph), Physics - Computational Physics, quantum computing, matrix inversion

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Access URL: http://arxiv.org/abs/2408.15453
https://zbmath.org/8021072
https://doi.org/10.1016/j.jcp.2025.113767

Random Toeplitz matrices: The condition number under high stochastic dependence: Random Toeplitz matrices: the condition number under high stochastic dependence

Authors: Paulo Manrique-Mirón

Source: Random Matrices: Theory and Applications. 11

Subject Terms: Random matrices (algebraic aspects), Toeplitz, Cauchy, and related matrices, random trigonometric polynomial, Numerical computation of matrix norms, conditioning, scaling, Probability (math.PR), small ball probability, Salem-Zygmund type inequality, Numerical Analysis (math.NA), 01 natural sciences, random Hankel matrix, decoupling, random Toeplitz matrix, random circulant matrix, Ill-posedness and regularization problems in numerical linear algebra, locally sub-Gaussian random variables, FOS: Mathematics, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Mathematics - Numerical Analysis, 0101 mathematics, Mathematics - Probability, condition number

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Access URL: http://arxiv.org/pdf/2005.09775
http://arxiv.org/abs/2005.09775
https://zbmath.org/7562974
https://doi.org/10.1142/s2010326322500277
https://worldscientific.com/doi/10.1142/S2010326322500277
https://dblp.uni-trier.de/db/journals/corr/corr2005.html#abs-2005-09775

PCM-TV-TFV: A Novel Two-Stage Framework for Image Reconstruction from Fourier Data: PCM-TV-TFV: a novel two-stage framework for image reconstruction from Fourier data

Authors: Guohui Song Yue Zhang Weihong Guo

Source: SIAM Journal on Imaging Sciences. 10:2250-2274

Subject Terms: FOS: Computer and information sciences, Numerical optimization and variational techniques, Convex programming, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, 02 engineering and technology, Fractional partial differential equations, 01 natural sciences, edge guided reconstruction, Fourier measurements, Ill-posedness and regularization problems in numerical linear algebra, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, total fractional order variation

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Access URL: http://arxiv.org/pdf/1705.10784
http://arxiv.org/abs/1705.10784
https://epubs.siam.org/doi/10.1137/17M1130666
https://dblp.uni-trier.de/db/journals/corr/corr1705.html#GuoSZ17
https://doi.org/10.1137/17M1130666
https://ui.adsabs.harvard.edu/abs/2017arXiv170510784G/abstract
https://arxiv.org/abs/1705.10784

Bayesian Abel Inversion in Quantitative X-Ray Radiography: Bayesian Abel inversion in quantitative X-ray radiography

Authors: Marylesa Howard Stephen Mitchell Aaron Luttman et al.

Source: SIAM Journal on Scientific Computing. 38:B396-B413

Subject Terms: Biomedical imaging and signal processing, inverse problems, Bayesian inference, Computational problems in statistics, maximum likelihood estimation, 16. Peace & justice, 01 natural sciences, Markov chain Monte Carlo, Ill-posedness and regularization problems in numerical linear algebra, X-ray radiography, Image processing (compression, reconstruction, etc.) in information and communication theory, 0101 mathematics, 10. No inequality, 0105 earth and related environmental sciences

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Access URL: https://www.osti.gov/biblio/1329259
http://dblp.uni-trier.de/db/journals/siamsc/siamsc38.html#HowardFLMH16
https://locus.siam.org/doi/abs/10.1137/15M1018721
https://dblp.uni-trier.de/db/journals/siamsc/siamsc38.html#HowardFLMH16
https://www.osti.gov/pages/biblio/1325541-bayesian-abel-inversion-quantitative-ray-radiography
https://epubs.siam.org/doi/10.1137/15M1018721

On the treatment of non-optimal regularization parameter influence on temperature distribution reconstruction accuracy in participating medium

Authors: Liu, Dong Yan, Jianhua Cen, Kefa

Source: International Journal of Heat and Mass Transfer. 55:1553-1560

Subject Terms: Numerical solutions to overdetermined systems, pseudoinverses, Least square QR decomposition method, Non-optimal, regularization parameter, least square QR decomposition method, 16. Peace & justice, 01 natural sciences, Temperature distribution, temperature distribution, Genetic algorithm, Ill-posedness and regularization problems in numerical linear algebra, Inverse radiation problem, Inverse problems in thermodynamics and heat transfer, Optimization problems in thermodynamics and heat transfer, truncated singular value decomposition method, 0103 physical sciences, genetic algorithm, inverse radiation problem, non-optimal regularization parameter, Truncated singular value decomposition method, 0105 earth and related environmental sciences

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Access URL: https://zbmath.org/6160309
https://doi.org/10.1016/j.ijheatmasstransfer.2011.11.010
https://www.sciencedirect.com/science/article/pii/S0017931011006478

Priorconditioners for linear systems

Authors: Daniela Calvetti Erkki Somersalo

Source: Inverse Problems. 21:1397-1418

Subject Terms: ill-posed problems, Iterative numerical methods for linear systems, numerical examples, Ill-posedness and regularization problems in numerical linear algebra, preconditioning, priorconditioners, Numerical computation of matrix norms, conditioning, scaling, iterative methods, convergence acceleration, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2215122
https://doi.org/10.1088/0266-5611/21/4/014
http://iopscience.iop.org/article/10.1088/0266-5611/21/4/014/pdf
https://iopscience.iop.org/article/10.1088/0266-5611/21/4/014/pdf
http://ui.adsabs.harvard.edu/abs/2005InvPr..21.1397C/abstract

Invertible smoothing preconditioners for linear discrete ill-posed problems

Authors: Daniela Calvetti Lothar Reichel A. Shuibi

Source: Applied Numerical Mathematics. 54:135-149

Subject Terms: Ill-posedness and regularization problems in numerical linear algebra, LSQR, Numerical computation of matrix norms, conditioning, scaling, Ill-posed problem, Preconditioning, RRGMRES, GMRES, 0101 mathematics, 01 natural sciences, Iterative method

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Access URL: https://dl.acm.org/doi/10.5555/1090567.1642743
https://www.sciencedirect.com/science/article/pii/S0168927404002004

Minimization of Linear Functionals Defined on Solutions of Large-Scale Discrete Ill-Posed Problems: Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems

Authors: Per Christian Hansen Lars Eldén Marielba Rojas

Source: BIT Numerical Mathematics. 45:329-340

Subject Terms: regularization, Numerical solutions to overdetermined systems, pseudoinverses, algorithm, Ill-posedness and regularization problems in numerical linear algebra, sideways heat equation, 0211 other engineering and technologies, 02 engineering and technology, 0101 mathematics, 01 natural sciences, discrete ill posed problems, confidence intervals

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Access URL: https://link.springer.com/article/10.1007/s10543-005-7122-y
http://core.ac.uk/display/24642336
http://sakai.wfu.edu/access/content/group/26f503c9-bec7-4bb7-bdab-82ed8fda9d39/publications/rojas/elden-hansen-rojas1.pdf
http://ta.twi.tudelft.nl/wagm/users/rojas/elden-hansen-rojas.pdf
http://www.diva-portal.org/smash/record.jsf?pid=diva2:243151

A classification scheme for regularizing preconditioners, with application to Toeplitz systems

Authors: Estatico, Claudio

Source: Linear Algebra and its Applications. 397:107-131

Subject Terms: Iterative numerical methods for linear systems, Numerical Analysis, Algebra and Number Theory, Ill-posed problems, Matrix algebras, Preconditioning, Regularization, Toeplitz matrices, Geometry and Topology, Discrete Mathematics and Combinatorics, Numerical computation of matrix norms, conditioning, scaling, regularizing preconditioners, linear systems, 01 natural sciences, numericl examples, Ill-posedness and regularization problems in numerical linear algebra, 0101 mathematics, matrix inverse

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Access URL: https://zbmath.org/2165351
https://doi.org/10.1016/j.laa.2004.10.006
https://www.sciencedirect.com/science/article/pii/S002437950400446X
https://www.sciencedirect.com/science/article/abs/pii/S002437950400446X
https://core.ac.uk/display/53550566
https://hdl.handle.net/11383/1719855
https://hdl.handle.net/11567/923950
https://doi.org/10.1016/j.laa.2004.10.006

Preconditioners Based on Fit Techniques for the Iterative Regularization in the Image Deconvolution Problem: Preconditioners based on fit techniques for the iterative regularization in the image deconvolution problem

Authors: Paola Favati Grazia Lotti Ornella Menchi et al.

Contributors: Paola Favati Grazia Lotti Ornella Menchi et al.

Source: BIT numerical mathematics (Dordr., Online) 45 (2005): 15–35. doi:10.1007/s10543-005-2639-7
info:cnr-pdr/source/autori:Paola Favati; Grazia Lotti; Ornella Menchi;/titolo:Preconditioners based on fit techniques for the iterative regularization in the image deconvolution problem/doi:10.1007%2Fs10543-005-2639-7/rivista:BIT numerical mathematics (Dordr., Online)/anno:2005/pagina_da:15/pagina_a:35/intervallo_pagine:15–35/volume:45

Subject Terms: Iterative numerical methods for linear systems, numerical examples, Numerical computation of matrix norms, conditioning, scaling, gradient-type iterations, 01 natural sciences, regularization, preconditioners, Ill-posedness and regularization problems in numerical linear algebra, image deconvolution, Toeplitz matrices, preconditioned gradient-type iterations, 0101 mathematics

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007%2Fs10543-005-2639-7
https://arpi.unipi.it/handle/11568/92644?mode=full.1
https://link.springer.com/content/pdf/10.1007/s10543-005-2639-7.pdf
http://www.springerlink.com/content/wx62u6j9177352pv/fulltext.pdf
https://doi.org/10.1007/s10543-005-2639-7
https://hdl.handle.net/20.500.14243/46147
https://hdl.handle.net/11568/92644
https://doi.org/10.1007/s10543-005-2639-7

Reviving the Method of Particular Solutions: Reviving the method of particular solutions

Authors: Timo Betcke Lloyd N. Trefethen

Source: SIAM Review. 47:469-491

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, numerical examples, Ill-posedness and regularization problems in numerical linear algebra, eigenmodes, method of particular solutions, eigenvalues, Spectral, collocation and related methods for boundary value problems involving PDEs, Laplacian, 0101 mathematics, 01 natural sciences, subspace angles

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Access URL: http://eprints.maths.manchester.ac.uk/589/1/MPSfinal.pdf
http://eprints.maths.manchester.ac.uk/589/
http://ui.adsabs.harvard.edu/abs/2005SIAMR..47..469B/abstract
https://dblp.uni-trier.de/db/journals/siamrev/siamrev47.html#BetckeT05
https://dl.acm.org/doi/10.1137/S0036144503437336
https://epubs.siam.org/doi/10.1137/S0036144503437336
http://eprints.ma.man.ac.uk/589/01/MPSfinal.pdf

Image restoration by cosine transform-based iterative regularization

Authors: Wilson C. Kwan Michael K. Ng

Source: Applied Mathematics and Computation. 160:499-515

Subject Terms: Ill-posedness and regularization problems in numerical linear algebra, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, Image processing (compression, reconstruction, etc.) in information and communication theory, 0101 mathematics, 01 natural sciences

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Access URL: https://dblp.uni-trier.de/db/journals/amc/amc160.html#NgK05
https://www.sciencedirect.com/science/article/pii/S0096300303011767

Distance to ill-posedness and the consistency value of linear semi-infinite inequality systems

Authors: Cánovas Cánovas, María Josefa López Cerdá, Marco A. Parra López, Juan et al.

Contributors: Cánovas Cánovas, María Josefa López Cerdá, Marco A. Parra López, Juan et al.

Source: Mathematical Programming. 103:95-126

Subject Terms: Linear inequality systems, regularity, distance to ill-posedness, Linear inequalities of matrices, 0211 other engineering and technologies, linear inequality systems, 02 engineering and technology, stability, ellipsoid algorithm, Regularity, Well-posedness, Ill-posedness and regularization problems in numerical linear algebra, Numerical mathematical programming methods, well-posedness, Estadística e Investigación Operativa, Linear programming, Inequalities and extremum problems involving convexity in convex geometry, Semi-infinite programming, Stability, Distance to ill-posedness

File Description: application/xml

Access URL: https://zbmath.org/2168042
https://doi.org/10.1007/s10107-004-0519-6
https://dblp.uni-trier.de/db/journals/mp/mp103.html#CanovasLPT05
http://rua.ua.es/dspace/handle/10045/75153
https://link.springer.com/article/10.1007/s10107-004-0519-6
https://doi.org/10.1007/s10107-004-0519-6
https://hdl.handle.net/10045/75153