Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations

DOI10.1002/nla.766zbMath1249.65087OpenAlexW2066549325MaRDI QIDQ2889380

Zi Cai Li, Hung-Tsai Huang, Yi-Min Wei

Publication date: 7 June 2012

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.766

zbMATH Keywords

Tikhonov regularizationtruncated singular value decompositionill-conditioningcollocation Trefftz methodeffective condition number

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (11)

The method of fundamental solutions for the Helmholtz equation ⋮ Neumann problems of 2D Laplace's equation by method of fundamental solutions ⋮ Neumann problems of Laplace's equation in circular domains with circular holes by methods of field equations ⋮ Some results on the regularization of LSQR for large-scale discrete ill-posed problems ⋮ A factorization of least-squares projection schemes for ill-posed problems ⋮ Algorithm singularity of the null-field method for Dirichlet problems of Laplace's equation in annular and circular domains ⋮ Cauchy problems of Laplace's equation by the methods of fundamental solutions and particular solutions ⋮ Analysis of the method of fundamental solutions for the modified Helmholtz equation ⋮ Regularized least squares locality preserving projections with applications to image recognition ⋮ Perturbation expansions and error bounds for the truncated singular value decomposition ⋮ Tikhonov Regularization and Randomized GSVD

Uses Software

• Regularization tools
• mctoolbox

Cites Work

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