Matrix analysis
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Max-min properties of matrix factor norms
SIAM Journal on Scientific Computing
Journal of Multivariate Analysis
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Exclusion and Inclusion Regions for the Eigenvalues of a Normal Matrix
SIAM Journal on Matrix Analysis and Applications
Orthogonal polyanalytic polynomials and normal matrices
Mathematics of Computation
Solution Methods for $\mathbb R$-Linear Problems in $\mathbb C^n $
SIAM Journal on Matrix Analysis and Applications
CMV matrices: Five years after
Journal of Computational and Applied Mathematics
Matrices, Moments and Quadrature with Applications
Matrices, Moments and Quadrature with Applications
Szego's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials (M. B. Porter Lectures)
Hi-index | 0.00 |
The speed of convergence of the R-linear GMRES method is bounded in terms of a polynomial approximation problem on a finite subset of the spectrum. This result resembles the classical GMRES convergence estimate except that the matrix involved is assumed to be condiagonalizable. The bounds obtained are applicable to the CSYM method, in which case they are sharp. Then a new three term recurrence for generating a family of orthogonal polynomials is shown to exist, yielding a natural link with complex symmetric Jacobi matrices. This shows that a mathematical framework analogous to the one appearing with the Hermitian Lanczos method exists in the complex symmetric case. The probability of being condiagonalizable is estimated with random matrices.