In the literature on regularization, many different parameter choice methods have been
proposed in both deterministic and stochastic settings. However, based on the available …

This paper surveys an important class of methods that combine iterative projection methods
and variational regularization methods for large-scale inverse problems. Iterative methods …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

This is the first book on constructive methods for, and applications of orthogonal
polynomials, and the first available collection of relevant Matlab codes. The book begins …

This computationally oriented book describes and explains the mathematical relationships
among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and …

Linear discrete ill-posed problems are difficult to solve numerically because their solution is
very sensitive to perturbations, which may stem from errors in the data and from round-off …

We describe a robust and adaptive implementation of the L-curve criterion. The algorithm
locates the corner of a discrete L-curve which is a log–log plot of corresponding residual …

Many numerical methods for the solution of linear ill-posed problems apply Tikhonov
regularization. This paper presents a new numerical method, based on Lanczos …

The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which
creeps into the mid and high degree and order harmonic coefficients of the Earth's monthly …

The Conjugate Gradient Method (CG) has an intrinsic regularization property when applied
to systems of linear equations with ill-conditioned matrices. This regularization property is …