MATRIX

Author: ALBERTÍ VILLALOBOS PEDRO ENRIQUE.
Year: 2004.
University: POLITÉCNICA DE VALENCIA [www.upv.es].
Place of defense: UNIVERSIDAD POLITÉCNICA DE VALENCIA.
Place of preparation: UNIVERSIDAD POLITÉCNICA DE VALENCIA.

Summary: One problem Own Back Securities (PIVP) is the reconstruction of a matrix from their spectral data (auto-valores or eigenvalues). The complexity of PIVP lies in building an array to keep certain specific characteristics of estructuta, and the characteristic spectral given. This thesis has been developed on the one hand a study of a type of problem that has no more than 20 ailos research in isolation to physical problem. The main objective of this thesis is the diseilo and implementing illgoritmos with parallel processing techniques, all the algorithms have a study and parallel implementation. The various algorithms developed in sequence at an early stage are improved algorithms presented by the scientific community and also presents algoritrnos sequential considered to be a new contribution to scientific research in this type of problem. So, in this way, this theory has been developed some aigoritmos sequential and parallel portable and efficient solve the problem Inverted Securities Own. In addition, it has tried algorithms obténidos are stable and provide comprehensive and accurate results. The implementations have been carried out sobre.una architecture parallel distributed high availability (clusters of PCs). Finally, it has been implemented successfully, a type of algorithm to solve problems Investors Additives Not Symmetrical securities Own a case study: the "problem of allocating poles."

Author: FLORES BECERRA GEORGINA.
Year: 2005.
University: POLITÉCNICA DE VALENCIA [www.upv.es].
Place of defense: UNIVERSIDAD POLITÉCNICA DE VALENCIA.
Place of preparation: UNIVERSIDAD POLITÉCNICA DE VALENCIA.

Summary: The reconstruction of a matrix with some structure and values unique is the so-called pre Problem Inverted Securities Singular (PIVS). This thesis addresses cases of PIVS as Problem Inverted Additive Securities Singular (PIAVS), the Problem Inverted Structured Securities Singular (PIEVS) and the Problem Inverted Securities Own Securities and Singular (PIVPVS). Developing routines efficient, robust and portable, both sequential and parallel has been the focus of this thesis. This objective is part of a wider goal is the design and implementation of digital libraries solve the problem Own Back Securities (PIVP), the PIVS and PIVPVS. This thesis has done a detailed study of theoretical and experimental methods currently available for the resolution of PIVs, methods that have been taken to resolve the PIVP and have adapted to the resolution of PIVS, and have also made approaches that solve the PIVS. The methods to solve the PIAVS have resulted in sequential and parallel iterative algorithms general. For PIEVS has redesigned a couple of methods of PIAVS to take advantage of the structure of the parent type Toeplitz that PIEVS handles, obtaining sequential and iterative algorithms highly efficient parallel. For PIVSVP have been proposed new iterative algorithms that build arrays extremely simple structures (matrices bidiagonales), which lead to easy and inexpensive management post. The implementations have been carried out on different parallel architectures, which includes parallel architectures and distributed memory parallel architectures of distributed shared memory. The algorithms have been designed routines implemented using libraries sequential numerical linear algebra (LAPACK, BLAS) and parallel (ScaLAPACK, PBLAS); for parallel implementations using message passing routines have been used for communicating bibiliotecas MPI and BLACS, while OpenMP directives have been used and parallel implementations of algorithms designed on the model of shared memory. The use of these tools ensures efficiency, robustness and portability of the algorithms implemented in this thesis.