Fiedler matrices: numerical and structural properties

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dc.contributor.advisor Terán Vergara, Fernando de
dc.contributor.advisor Martínez Dopico, Froilán César Pérez Álvaro, Javier 2015-10-22T14:00:55Z 2015-10-22T14:00:55Z 2015-04 2015-06-18
dc.description.abstract The first and second Frobenius companion matrices appear frequently in numerical application, but it is well known that they possess many properties that are undesirable numerically, which limit their use in applications. Fiedler companion matrices, or Fiedler matrices for brevity, introduced in 2003, is a family of matrices which includes the two Frobenius matrices. The main goal of this work is to study whether or not Fiedler companion matrices can be used with more reliability than the Frobenius ones in the numerical applications where Frobenius matrices are used. For this reason, in this work we present a thorough study of Fiedler matrices: their structure and numerical properties, where we mean by numerical properties those properties that are interesting for applying these matrices in numerical computations, and some of their applications in the field on numerical linear algebra. The introduction of Fiedler companion matrices is an example of a simple idea that has been very influential in the development of several lines of research in the numerical linear algebra field. This family of matrices has important connections with a number of topics of current interest, including: polynomial root finding algorithms, linearizations of matrix polynomials, unitary Hessenberg matrices, CMV matrices, Green’s matrices, orthogonal polynomials, rank structured matrices, quasiseparable and semiseparable matrices, etc.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Numerical linear algebra
dc.subject.other Matrix analysis
dc.subject.other Frobenius matrices
dc.subject.other Fiedler matrices
dc.title Fiedler matrices: numerical and structural properties
dc.type doctoralThesis
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess Programa Oficial de Doctorado en Ingeniería Matemática
dc.description.responsability Presidente: Paul Van Dooren.- Secretario: Juan Bernardo Zaballa Tejada.- Vocal: Françoise Tisseur
dc.contributor.departamento Universidad Carlos III de Madrid. Departamento de Matemáticas
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