A Flexible Krylov Solver for Shifted Systems with Application to Oscillatory Hydraulic Tomography

DOI10.1137/120902690zbMath1288.65041arXiv1212.3660OpenAlexW3104443378MaRDI QIDQ5404623

Tania Bakhos, Peter K. Kitanidis, Arvind K. Saibaba

Publication date: 28 March 2014

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.3660

zbMATH Keywords

algorithminverse problemsgeneralized eigenvalue problempreconditionernumerical experimentArnoldi methodKrylov solversgeneralized minimal residual (GMRES)shifted systemsfull orthogonal method (FOM)oscillatory hydraulic tomography

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Hydrology, hydrography, oceanography (86A05) Inverse problems in geophysics (86A22) Iterative numerical methods for linear systems (65F10) Computational methods for problems pertaining to geophysics (86-08) Preconditioners for iterative methods (65F08)

Related Items (20)

An efficient two-level preconditioner for multi-frequency wave propagation problems ⋮ Nested Krylov Methods for Shifted Linear Systems ⋮ Restarted Hessenberg method for solving shifted nonsymmetric linear systems ⋮ A new shifted block GMRES method with inexact breakdowns for solving multi-shifted and multiple right-hand sides linear systems ⋮ A shifted block FOM algorithm with deflated restarting for matrix exponential computations ⋮ Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM ⋮ A flexible and adaptive simpler GMRES with deflated restarting for shifted linear systems ⋮ GMRES algorithms over 35 years ⋮ Multipreconditioned Gmres for Shifted Systems ⋮ An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies ⋮ Less is often more: applied inverse problems using \(hp\)-forward models ⋮ Computing Reduced Order Models via Inner-Outer Krylov Recycling in Diffuse Optical Tomography ⋮ Flexible and deflated variants of the block shifted GMRES method ⋮ A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers ⋮ Non-cooperative finite element games ⋮ On restarted and deflated block FOM and GMRES methods for sequences of shifted linear systems ⋮ A flexible global GCRO-DR method for shifted linear systems and general coupled matrix equations ⋮ Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously ⋮ Flexible Krylov Methods for $\ell_p$ Regularization ⋮ Preconditioning Parametrized Linear Systems

Uses Software

• DOLFIN
• PyAMG

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