This thesis deals with the development of efficient and reliable algorithms and library software for factorizing matrices and solving matrix equations on high-performance computer systems. The architectures of today's computers consist of multiple processors, each with multiple functional units. The memory systems are hierarchical with several levels, each having different speed and size. The practical peak performance of a system is reached only by considering all of these characteristics. One portable method for achieving good system utilization is to express a linear algebra problem in terms of level 3 BLAS (Basic Linear Algebra Subprogram) transformations. The most important operation is GEMM (GEneral Matrix Multiply), which typically defines the practical peak performance of a computer system. There are efficient GEMM implementations available for almost any platform, thus an algorithm using this operation is highly portable. The dissertation focuses on how recursion can be applied to solve linear algebra problems. Recursive linear algebra algorithms have the potential to automatically match the size of subproblems to the different memory hierarchies, leading to much better utilization of the memory system. Furthermore, recursive algorithms expose level 3 BLAS operations, and reveal task parallelism. The first paper handles the Cholesky factorization for matrices stored in packed format. Our algorithm uses a recursive packed matrix data layout that enables the use of high-performance matrix--matrix multiplication, in contrast to the standard packed format. The resulting library routine requires half the memory of full storage, yet the performance is better than for full storage routines. Paper two and tree introduce recursive blocked algorithms for solving triangular Sylvester-type matrix equations. For these problems, recursion together with superscalar kernels produce new algorithms that give 10-fold speedups compared to existing routines in the SLICOT and LAPACK libraries. We show that our recursive algorithms also have a significant impact on the execution time of solving unreduced problems and when used in condition estimation. By recursively splitting several problem dimensions simultaneously, parallel algorithms for shared memory systems are obtained. The fourth paper introduces a library---RECSY---consisting of a set of routines implemented in Fortran 90 using the ideas presented in paper two and three. Using performance monitoring tools, the last paper evaluates the possible gain in using different matrix blocking layouts and the impact of superscalar kernels in the RECSY library.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-04-25T17:30:25Z No. of bitstreams: 1 carloshenriquenascimentomartins.pdf: 10221613 bytes, checksum: 0d6eef0f715fc0f9f68bf12a390dcd55 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-04-26T12:22:24Z (GMT) No. of bitstreams: 1 carloshenriquenascimentomartins.pdf: 10221613 bytes, checksum: 0d6eef0f715fc0f9f68bf12a390dcd55 (MD5) / Made available in DSpace on 2017-04-26T12:22:24Z (GMT). No. of bitstreams: 1 carloshenriquenascimentomartins.pdf: 10221613 bytes, checksum: 0d6eef0f715fc0f9f68bf12a390dcd55 (MD5) Previous issue date: 2015-03-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta tese apresenta as etapas de desenvolvimento de um sistema de monitoramento de parâmentos de qualidade de energia dedicado a análise de harmônicos variantes no tempo através do equipamento denominado AHVT (Analisador de Harmônicos Variantes no Tempo). O desenvolvimento do trabalho é composto por: (i) estudo e implementação MATLAB de algoritmos para processamento em tempo real, com capacidade de sintonização dos componentes harmônicos; (ii) análise e desenvolvimento de estratégias para detecção e validação da presença de interharmônicos próximos à frequência fundamental e suas consequência na estimação de parâmetros como fase, amplitude e frequência para o componente fundamental, (iii) proposta de implementação do dispositivo, sistema de aquisição/ condicionamento de sinais/ filtragem, sistema de conversão analógico digital e plataforma de processamentoDSP/FPGA, sistema de transmissão de dados e plataformas de análise online/offline dos eventos de harmônicos variantes no tempo; (iv) plataforma de simulação do Analisador de Harmônicos Variantes no Tempo (AHVT) para estudo dos métodos de trigger para detecção e captura dos eventos. / In this work is presented the steps of development and implementation of a Power Quality paramaters monitoring system with main goal events denomined ”time arying harmonics”named of Time Varying Harmonic Analyzer. The development is comprises:(i) research and implementation of real time algorithms with capable to tuning harmonic waves,(ii) Analyze and research/development of strategies for detect and validation of interharmonics with frequencies near of fundamental, and conseguencies and challenges to phase, magnitude and frequency estimation with presence interharmonic waveform (iii) The proposal of a hardware design including analog to digital conversion and digital signal processing plataform, broadcast data link and IHM(Interface Human Machine) for online and offline analyzes to time varying harmonic analyzer;(iiii)off-line simulation plataform of Analisador de Harmônicos Variantes no Tempo Time Varying Harmonic Analyzer (TVHA) to trigger detect methods to detection and capture of waveforms.

Tato diplomová práce nastiňuje teoretické základy potřebné pro návrh algoritmu rekurzivní metody nejmenších čtverců a následně jeho aplikaci na experimentální data naměřená při testovacím manévru uskutečněném v roce 2001. Analyzována byla příčná dynamika jednostopého rovinného modelu vozidla. Práce také obsahuje srovnání výsledků získaných jednak rekurzivním algoritmem a dále i algoritmem Kalmanova filtru.