Laguerre matrix polynomial series expansion: Theory and computer applications

• Published in: Mathematical and computer modelling Vol. 44; no. 11; pp. 1025 - 1043
• Main Authors: Sastre, J., Defez, E., Jódar, L.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.12.2006; Elsevier Science
• Subjects: Asymptotic expression; Differential systems; Exact sciences and technology; Laguerre matrix polynomial; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Numerical linear algebra; Ordinary differential equations; Sciences and techniques of general use; Series expansion; Series expansion; Asymptotic expression; Differential systems; Laguerre matrix polynomial; Computer theory; Differential equation; Differential system; Numerical linear algebra; Hermitian matrix; Laguerre polynomial; Matrix function; Direct method; Numerical analysis; Linear system; Matrix inversion; Applied mathematics; Computer applications; Matrix polynomial; Asymptotic approximation; Complex matrix
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2006.03.006

This paper deals with the expansion of matrix functions in series of Laguerre matrix polynomials of a complex matrix parameter. A new asymptotic expression for positive and large x and n is obtained for this family of matrix polynomials that improves previous existing expressions. This expression is applied to improving the conditions imposed on the matrix function that are to be expanded in a series of non-hermitian Laguerre matrix polynomials, providing a new series expansion theorem that is more general than previous works. An application to solving linear differential systems without matrix exponentials is included.