Abstract
Some numerical algorithms for computing eigenvalues of nonsymmetric matrix
with high accuracy have been recently designed based on the discrete hungry Toda equation
and the discrete Lotka-Volterra system which are known as the discrete integrable systems
of hungry type. In this paper, not only the process for formulating these algorithms but
also the results concerning asymptotic analysis through the center manifold theory, mixed
error analysis in
oating point arithmetic and shift of origin for accelerating convergence
are shortly explained. Backlund transformations between discrete integrable systems of
hungry type are also shown.
with high accuracy have been recently designed based on the discrete hungry Toda equation
and the discrete Lotka-Volterra system which are known as the discrete integrable systems
of hungry type. In this paper, not only the process for formulating these algorithms but
also the results concerning asymptotic analysis through the center manifold theory, mixed
error analysis in
oating point arithmetic and shift of origin for accelerating convergence
are shortly explained. Backlund transformations between discrete integrable systems of
hungry type are also shown.
| Translated title of the contribution | Discrete Integrable Systems of Hungry Type and Numerical Algorithms for Eigenvalues of Nonsymmetric Matrices: Recent Developments in Integrable Algorithms |
|---|---|
| Original language | Japanese |
| Pages (from-to) | 109-181 |
| Journal | Transactions of the Japan Society for Industrial and Applied Mathematics |
| Volume | 23 |
| Publication status | Published - 2013 |