The symmetric eigenvalue problem
The symmetric eigenvalue problem
How to choose modified moments?
Journal of Computational and Applied Mathematics
Accurate recovery of recursion coefficients from Gaussian quadrature formulas
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Stability Estimates on the Jacobi and Unitary Hessenberg Inverse Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
Stability of passing from Gaussian quadrature data to the Lanczos recurrence coefficients is considered. Special attention is paid to estimates explicitly expressed in terms of quadrature data and not having weights in denominators. It has been shown that the recent approach, exploiting integral representation of Hankel determinants, implies quantitative improvement of D. Laurie's constructive estimate. It has also been demonstrated that a particular implementation on the Hankel determinant approach gives an estimate being unimprovable up to a coefficient; the corresponding example involves quadrature data with a small but not too small weight. It follows that polynomial increase of a general case upper bound in terms of the dimension is unavoidable.