We discuss the solution of numerically ill-posed overdetermined systems of equations using Tikhonov a-priori-based regularization. When the noise distribution on the measured data is available to appropriately weight the fidelity term, and the regularization is assumed to be weighted by inverse covariance information on the model parameters, the underlying cost functional becomes a random varia...

In this paper we propose an algorithm for solving the large-scale discrete ill-conditioned linear problems arising from the discretization of linear or nonlinear inverse problems. The algorithm combines some existing regularization techniques and regularization parameter choice rules with a randomized singular value decomposition (SVD) so that only much smaller-scale systems are needed to solve...

This paper is concerned with the computation of accurate approximate solutions of linear systems of equations and linear least-squares problems with a very ill-conditioned matrix and error-contaminated data. The solution of this kind of problems requires regularization. Common regularization methods include the truncated singular value decomposition and truncated iteration with a Krylov subspac...

Ill-posedness of GNSS-based ionospheric tomography affects the stability and accuracy inversion results. Truncated singular value decomposition (TSVD) is a common algorithm reconstruction. However, TSVD method usually has low reconstruction efficiency. To resolve above problem, truncated mapping (TMSVD) presented to improve reconstructed computational authenticate effectiveness advantages TMSVD...

The method of truncated total least squares [2] is an alternative to the classical truncated singular value decomposition used for the regularization of ill-conditioned linear systems Ax ≈ b [3]. Truncation methods aim at limiting the contribution of noise or rounding errors by cutting off a certain number of terms in an expansion such as the singular value decomposition. To this end a truncati...

The random volume over ground (RVoG) model associates vegetation vertical structure parameters with multiple complex interferometric coherence observables. In this paper, on the basis of the RVoG model, a truncated singular value decomposition (TSVD)-based method is proposed for forest height inversion from single-baseline polarimetric interferometric synthetic aperture radar (PolInSAR) data. I...

In this paper Legendre wavelet bases have been used for finding approximate solutions to singular boundary value problems arising in physiology. When the number of basis functions are increased the algebraic system of equations would be ill-conditioned (because of the singularity), to overcome this for large $M$, we use some kind of Tikhonov regularization. Examples from applied sciences are pr...

The truncated singular value decomposition (TSVD) is a popular method for solving linear discrete ill-posed problems with small to moderately sized matrix A. This replaces the A by closest Ak of low rank k, and then computes minimal norm solution system equations rank-deficient so obtained. modified TSVD (MTSVD) improves method, replacing that closer than in unitarily invariant has same spectra...

Abstract. For large-scale symmetric discrete ill-posed problems, MINRES and MR-II are commonly used iterative solvers. In this paper, we analyze their regularizing effects. We first prove that the regularized solutions by MINRES have filtered SVD forms. Then we show that (i) a hybrid MINRES that uses explicit regularization within projected problems is generally needed to compute a best possibl...