## 2017.23: Linearizations of Matrix Polynomials in Newton Bases

2017.23:
Vasilije Perovic and D. Steven Mackey
(2017)
*Linearizations of Matrix Polynomials in Newton Bases.*

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 446 Kb |

## Abstract

We discuss matrix polynomials expressed in a Newton basis, and the associated polynomial eigenvalue problems. Properties of the generalized ansatz spaces associated with such polynomials are proved directly by utilizing a novel representation of pencils in these spaces. Also, we show how the family of Fiedler pencils can be adapted to matrix polynomials expressed in a Newton basis. These new Newton-Fiedler pencils are shown to be strong linearizations, and some computational aspects related to them are discussed.

Item Type: | MIMS Preprint |
---|---|

Uncontrolled Keywords: | matrix polynomial, Newton bases, strong linearization, Newton-Fiedler pencil, ansatz space, updating |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 41 Approximations and expansions MSC 2000 > 65 Numerical analysis |

MIMS number: | 2017.23 |

Deposited By: | Dr. D. Steven Mackey |

Deposited On: | 18 July 2017 |

Download Statistics: last 4 weeks

Repository Staff Only: edit this item