The computational solution of problems can be restricted by the availability of solution
methods for linear (ized) systems of equations. In conjunction with 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 …

When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

It is well known that the trapezoidal rule converges geometrically when applied to analytic
functions on periodic intervals or the real line. The mathematics and history of this …

Given the square matrices A,B,D,E and the matrix C of conforming dimensions, we consider
the linear matrix equation A\mathbfXE+D\mathbfXB=C in the unknown matrix \mathbfX. Our …

The study presents a thermal runaway propagation (TRP) model developed by coupling the
reduced-order thermal and thermal runaway (TR) models at the mini-module, real-module …

In this paper we propose a new projection method to solve large-scale continuous-time
Lyapunov matrix equations. The new approach projects the problem onto a much smaller …

The quantification of probabilistic uncertainties in the outputs of physical, biological, and
social systems governed by partial differential equations with random inputs require, in …

Although the deep learning technique has been introduced into computational physics in
recent years, the feasibility of applying it to solve electromagnetic (EM) scattering field from …

We provide a new robust convergence analysis of the well-known power method for
computing the dominant singular vectors of a matrix that we call noisy power method. Our …