GCV for Tikhonov regularization by partial SVD
From MaRDI portal
Publication:1689313
DOI10.1007/s10543-017-0662-0zbMath1386.65118OpenAlexW2616678780MaRDI QIDQ1689313
Hassane Sadok, Giuseppe Rodriguez, Caterina Fenu, Lothar Reichel
Publication date: 12 January 2018
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10543-017-0662-0
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22)
Related Items (26)
Estimates for the generalized cross-validation function via an extrapolation and statistical approach ⋮ On the computation of a truncated SVD of a large linear discrete ill-posed problem ⋮ Fractional Tikhonov regularization to improve the performance of extreme learning machines ⋮ Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations ⋮ Stable Computation of Least Squares Problems of the OGM(1,N) Model and Short-Term Traffic Flow Prediction ⋮ Parameter determination for Tikhonov regularization problems in general form ⋮ Automatic fidelity and regularization terms selection in variational image restoration ⋮ Golub-Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems ⋮ Generalized cross validation for \(\ell^p\)-\(\ell^q\) minimization ⋮ A special modified Tikhonov regularization matrix for discrete ill-posed problems ⋮ Graph Laplacian for image deblurring ⋮ A Zeroth-Order Proximal Stochastic Gradient Method for Weakly Convex Stochastic Optimization ⋮ Determination of regularization parameter via solving a multi-objective optimization problem ⋮ Estimating the trace of matrix functions with application to complex networks ⋮ Adaptive cross approximation for Tikhonov regularization in general form ⋮ Variable projection methods for separable nonlinear inverse problems with general-form Tikhonov regularization ⋮ ADMM-based residual whiteness principle for automatic parameter selection in single image super-resolution problems ⋮ Approximation of the Tikhonov regularization parameter through Aitken's extrapolation ⋮ Heuristic Parameter Choice Rules for Tikhonov Regularization with Weakly Bounded Noise ⋮ The extended global Lanczos method for matrix function approximation ⋮ Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition ⋮ Simple stopping criteria for the LSQR method applied to discrete ill-posed problems ⋮ Extended nonsymmetric global Lanczos method for matrix function approximation ⋮ A comparison of parameter choice rules for \(\ell^p\)-\(\ell^q\) minimization ⋮ Color image and video restoration using tensor CP decomposition ⋮ An efficient Gauss-Newton algorithm for solving regularized total least squares problems
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A GCV based Arnoldi-Tikhonov regularization method
- \texttt{smt}: A Matlab toolbox for structured matrices
- A Krylov-Schur approach to the truncated SVD
- A note on the computation of the generalized cross-validation function for ill-conditioned least squares problems
- Restarted block Lanczos bidiagonalization methods
- A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations
- Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
- A weighted pseudoinverse, generalized singular values, and constrained least squares problems
- Analysis of directed networks via partial singular value decomposition and Gauss quadrature
- On Krylov projection methods and Tikhonov regularization
- On the computation of a truncated SVD of a large linear discrete ill-posed problem
- An implicitly restarted block Lanczos bidiagonalization method using Leja shifts
- Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems
- Estimations of the trace of powers of positive self-adjoint operators by extrapolation of the moments
- Regularization tools version \(4.0\) for matlab \(7.3\)
- Some large-scale matrix computation problems
- Harmonic and refined extraction methods for the singular value problem, with applications in least squares problems
- Orthogonal projection regularization operators
- A Jacobi--Davidson Type SVD Method
- GCV for Tikhonov regularization via global Golub–Kahan decomposition
- Moments of a linear operator, with applications to the trace of the inverse of matrices and the solution of equations
- Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
- A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines
- Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
- A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
- Rank-Deficient and Discrete Ill-Posed Problems
- An Implicitly Restarted Refined Bidiagonalization Lanczos Method for Computing a Partial Singular Value Decomposition
- A probing method for computing the diagonal of a matrix inverse
- A Method for Generating Infinite Positive Self-adjoint Test Matrices and Riesz Bases
This page was built for publication: GCV for Tikhonov regularization by partial SVD