Matrix analysis
Updating and downdating of orthogonal polynomials with data fitting applications
SIAM Journal on Matrix Analysis and Applications
Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation
SIAM Journal on Matrix Analysis and Applications
Convergence of iterations for linear equations
Convergence of iterations for linear equations
Vector Orthogonal Polynomials and Least Squares Approximation
SIAM Journal on Matrix Analysis and Applications
Polynomial interpolation in several variables
Studies in computer science
Matrix computations (3rd ed.)
Applied numerical linear algebra
Applied numerical linear algebra
A Stratification of the Set of Normal Matrices
SIAM Journal on Matrix Analysis and Applications
A Hermitian Lanczos Method for Normal Matrices
SIAM Journal on Matrix Analysis and Applications
Full length article: Orthogonal polynomials of the R-linear generalized minimal residual method
Journal of Approximation Theory
| Hi-index | 0.00 |
The Hermitian Lanczos method for Hermitian matrices has a well-known connection with a 3-term recurrence for polynomials orthogonal on a discrete subset of R. This connection disappears for normal matrices with the Arnoldi method. In this paper we consider an iterative method that is more faithful to the normality than the Arnoldi iteration. The approach is based on enlarging the set of polynomials to the set of polyanalytic polynomials. Denoting by d the number of elements computed so far, the arising scheme yields a recurrence of length bounded by √8d for polyanalytic polynomials orthogonal on a discrete subset of C. Like this slowly growing length of the recurrence, the method preserves, at least partially, the properties of the Hermitian Lanczos method. We employ the algorithm in least squares approximation and bivariate Lagrange interpolation.