Author:
Mainar E.,Peña J. M.,Rubio B.
Abstract
AbstractBidiagonal factorizations for the change of basis matrices between monomial and Newton polynomial bases are obtained. The total positivity of these matrices is characterized in terms of the sign of the nodes of the Newton bases. It is shown that computations to high relative accuracy for algebraic problems related to these matrices can be achieved whenever the nodes have the same sign. Stirling matrices can be considered particular cases of these matrices, and then computations to high relative accuracy for collocation and Wronskian matrices of Touchard polynomial bases can be obtained. The performed numerical experimentation confirms the accurate solutions obtained when solving algebraic problems using the proposed factorizations, for instance, for the calculation of their eigenvalues, singular values, and inverses, as well as the solution of some linear systems of equations associated with these matrices.
Publisher
Springer Science and Business Media LLC
Reference33 articles.
1. Ando, T.: Totally positive matrices. Linear Algebra Appl. 90, 165–219 (1987)
2. Barreras, A., Peña, J.M.: Accurate computations of matrices with bidiagonal decomposition using methods for totally positive matrices. Numer. Linear Algebra Appl. 20, 413–424 (2013)
3. de Boor, C.: A practical guide to splines. Springer-Verlag, New York (1978)
4. $$\mathring{A}$$. Björck, V. Pereyra, Solution of Vandermonde systems of equations, Math. Comp. 24 893–903 (1970)
5. J.M. Carnicer, Y. Khiar, J.M. Peña, Factorization of Vandermonde matrices and the Newton formula, Monografias Matemáticas Garcáa de Galdeano 40 53–60 (2015)
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