Accurate and fast computations with positive extended Schoenmakers–Coffey matrices

Schoenmakers–Coffey matrices are correlation matrices with important financial applications. Several characterizations of positive extended Schoenmakers–Coffey matrices are presented. This paper provides an accurate and fast method to obtain the bidiagonal decomposition of the conversion of these matrices, which in turn can be used to compute with high relative accuracy the eigenvalues and inverses of positive extended Schoenmakers–Coffey matrices. Numerical examples are included

Accurate and fast computations with Green matrices

This paper provides a linear time complexity method to obtain the bidiagonal decomposition of Green matrices with high relative accuracy. In addition, when the Green matrix is nonsingular and totally positive, this bidiagonal decomposition can be used to compute the eigenvalues, the inverse and the solution of some linear system of equations with high relative accuracy. A numerical example illustrates the advantages of this method

Algorithms for curve design and accurate computations with totally positive matrices

Esta tesis doctoral se enmarca dentro de la teoría de la Positividad Total. Las matrices totalmente positivas han aparecido en aplicaciones de campos tan diversos como la Teoría de la Aproximación, la Biología, la Economía, la Combinatoria, la Estadística, las Ecuaciones Diferenciales, la Mecánica, el Diseño Geométrico Asistido por Ordenador o el Álgebra Numérica Lineal. En esta tesis nos centraremos en dos de los campos que están relacionados con matrices totalmente positivas.This doctoral thesis is framed within the theory of Total Positivity. Totally positive matrices have appeared in applications from fields as diverse as Approximation Theory, Biology, Economics, Combinatorics, Statistics, Differential Equations, Mechanics, Computer Aided Geometric Design or Linear Numerical Algebra. In this thesis, we will focus on two of the fields that are related to totally positive matrices.<br /