The main purpose of this paper is to show that linear least squares methods based on bidiagonalization, namely the LSQR algorithm, can be used for generation of trust region path. This property is a basis for an inexact trust region method which uses the LSQR algorithm for direction determination. This method is very efficient for large sparse nonlinear least squares as it is supported by numer...

We present experiments with various solvers for large sparse matrix eigenvalue problems. These problems occur in the computation of a few of the lowest frequencies of standing electromagnetic waves in cavities that have been discretized by the nite element method. The solvers investigated are (1) subspace iteration, (2) block Lanczos algorithm, (3) implicitly restarted Lanczos algorithm and (4)...

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163–171]. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiven...

In inverse problem of electrocardiography (ECG), electrical activity of the heart is estimated from body surface potential measurements. This electrical activity provides useful information about the state of the heart, thus it may help clinicians diagnose and treat heart diseases before they cause serious health problems. For practical application of the method, having fewer number of electrod...

The biorthogonal Lanczos and the biconjugate gradient methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld (1989) obtained the conjugate gradient squared by squaring the matrix polynomials of the biconjugate gradient method. Here we square the unsymmetric (or biorthogonal) Lanczos method for computing the eigenvalue...

The power method and block Lanczos method are popular numerical algorithms for computing the truncated singular value decomposition (SVD) and eigenvalue decomposition problems. Especially in the literature of randomized numerical linear algebra, the power method is widely applied to improve the quality of randomized sketching, and relative-error bounds have been well established. Recently, Musc...