Golub-Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems
DOI10.1007/s10543-021-00857-0zbMath1490.65066OpenAlexW3147334223MaRDI QIDQ2665542
Alessandro Buccini, Xianglan Bai, Lothar Reichel
Publication date: 19 November 2021
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10543-021-00857-0
Tikhonov regularizationdiscrepancy principlediscrete ill-posed problemGolub-Kahan bidiagonalizationrandomized SVD
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Regularization matrices determined by matrix nearness problems
- Arnoldi methods for image deblurring with anti-reflective boundary conditions
- On the choice of solution subspace for nonstationary iterated Tikhonov regularization
- Invertible smoothing preconditioners for linear discrete ill-posed problems
- An iterative method for Tikhonov regularization with a general linear regularization operator
- A new zero-finder for Tikhonov regularization
- Arnoldi-Tikhonov regularization methods
- Regularization methods for large-scale problems
- Tikhonov regularization of large linear problems
- GCV for Tikhonov regularization by partial SVD
- A weighted pseudoinverse, generalized singular values, and constrained least squares problems
- Old and new parameter choice rules for discrete ill-posed problems
- Estimation of the \(L\)-curve via Lanczos bidiagonalization
- Square smoothing regularization matrices with accurate boundary conditions
- A simplified L-curve method as error estimator
- Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems
- On Krylov projection methods and Tikhonov regularization
- IR tools: a MATLAB package of iterative regularization methods and large-scale test problems
- Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems
- Regularization tools version \(4.0\) for matlab \(7.3\)
- Improvement of the resolution of an instrument by numerical solution of an integral equation
- Regularization with randomized SVD for large-scale discrete inverse problems
- Deblurring Images
- Randomized algorithms for large-scale inverse problems with general Tikhonov regularizations
- A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
- Determining Surface Temperatures from Interior Observations
- Rank-Deficient and Discrete Ill-Posed Problems
- Regularization matrices for discrete ill‐posed problems in several space dimensions
This page was built for publication: Golub-Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems
