From numerical quadrature to Padé approximation
Applied Numerical Mathematics
Computers & Mathematics with Applications
Spectral Methods for Parameterized Matrix Equations
SIAM Journal on Matrix Analysis and Applications
Computing $f(A)b$ via Least Squares Polynomial Approximations
SIAM Journal on Scientific Computing
On Efficient Numerical Approximation of the Bilinear Form $c^*A^{-1}b$
SIAM Journal on Scientific Computing
Estimates of the Norm of the Error in Solving Linear Systems with FOM and GMRES
SIAM Journal on Scientific Computing
Preconditioning for Allen-Cahn variational inequalities with non-local constraints
Journal of Computational Physics
dqds with Aggressive Early Deflation
SIAM Journal on Matrix Analysis and Applications
Full length article: Orthogonal polynomials of the R-linear generalized minimal residual method
Journal of Approximation Theory
Old and new parameter choice rules for discrete ill-posed problems
Numerical Algorithms
Block conjugate gradient type methods for the approximation of bilinear form CHA-1B
Computers & Mathematics with Applications
Hi-index | 0.00 |
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part.Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization.This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.