Linearization of Lagrange and Hermite interpolating matrix polynomials
نویسندگان
چکیده
منابع مشابه
Linearization of Lagrange and Hermite interpolating matrix polynomials
This paper considers interpolating matrix polynomials P (λ) in Lagrange and Hermite bases. A classical approach to investigate the polynomial eigenvalue problem P (λ)x = 0 is linearization, by which the polynomial is converted into a larger matrix pencil with the same eigenvalues. Since the current linearizations of degree n Lagrange polynomials consist of matrix pencils with n + 2 blocks, they...
متن کاملOn Hermite-hermite Matrix Polynomials
In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite ma...
متن کاملLinearization of regular matrix polynomials
This note contains a short review of the notion of linearization of regular matrix polynomials. The objective is clarification of this notion when the polynomial has an “eigenvalue at infinity”. The theory is extended to admit reduction by locally unimodular analytic matrix functions.
متن کاملOn linearization and connection coefficients for generalized Hermite polynomials
We consider the problem of finding explicit formulae, recurrence relations and sign properties for both connection and linearization coefficients for generalized Hermite polynomials. The most computations are carried out by the computer algebra system Maple using appropriate algorithms.
متن کاملA Simple Algorithm for the Construction of Lagrange and Hermite Interpolating Polynomial in Two Variables
A simple algorithm for the construction of the unique Hermite interpolating polynomial (in the special case, the Lagrange interpolating polynomial) is given. The interpolation matches preassigned data of function and consecutive derivatives on a set of points laying on several radial rays. This algorithm is realized in the software package Mathematica.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2014
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/dru019