## Abstract

The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and well-free Vandermonde-like matrices having * O(n2) * complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2-term and 3-term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and well-free polynomials. Finally we present an * O(n2) * algorithm to compute the inversion of quasiseparable Vandermonde-like matrices.

Original language | American English |
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Journal | Cornell University Library |

State | Published - Jan 9 2014 |

## Keywords

- Quasiseparable matrix
- Fast algorithms
- Inversion algorithms

## Disciplines

- Controls and Control Theory
- Numerical Analysis and Computation
- Numerical Analysis and Scientific Computing
- Signal Processing
- Theory and Algorithms