A perturbation analysis shows that if a numerically stable procedure is used to compute the matrix sign function, then it is competitive with conventional methods for computing invariant subspaces. Stability analysis of the Newton iteration improves an earlier result of Byers and confirms that ill-conditioned iterates may cause numerical instability. Numerical examples demonstrate the theoretical results.

We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and performance of the resulting methods with existing Sylvester solvers. The algorithms proposed here are easy to parallelize. We report on the parallelization of those algorithms and demonstrate their high efficiency and scalability using experimental results obtained on a cluster of Intel Pentium Xeon processors.

Made available in DSpace on 2016-04-26T18:18:34Z (GMT). No. of bitstreams: 1 Tarcisio de Sa Cardoso.pdf: 5324585 bytes, checksum: 0a2380896645c26954804659ea1cba01 (MD5) Previous issue date: 2010-05-14 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / This research seeks to understand the mechanisms of non-representational contemporary graphic design. The expression "non-representative" is intended to connote some kind of sign that is characterized by polysemy. In print, this aspect has insisted to emerge in many different manifestations. Despite its recurrence, this type of sign has not received the deserved attention by the scientific community, especially in regarding to the theory of signs an instrument that seems privileged to explain the functions of language presented there. Called unreadable and dysfunctional, the graphic design of David Carson, Neville Brody, Edward Fella, April Greiman and many others are still currently subject of contents. To be more specific, we may say that all post-ulmian vanguard from around the world, questions the rationality of an area so close to the arts, and represents a kind of counterpoint to the canonical approach, which from the Bauhaus and constructivism tries to articulate an exclusivist disciplinarity to the design. This objection became important especially in Europe (HOLLIS, 2001) and in the USA (MCCOY, 1990), in which new wave movement has its most characteristic representation. One of the theorists that works with the evolution of the modernist slogan form follows function, Bürdek presents the problem of function in a new outlook not anymore as an exclusively practical function, but mainly what he called a sign function. According to him, these are the most important functions for design (BÜRDEK, 2002). From this point of view, we intend to answer how these sign functions are articulated in visuality of post-modern design from the 1990s, to build communication processes that dialogue with the culture of information, or the culture in which the sign function overcome the function of use (BAUDRILLARD, 1995). Differently from the structuralist conception of the sign in Baudrillard it means by sign function, in this study, the processes that substantiate the sign according to Peirce's semiotics (on aspects of quality, existence and regularity). From this perspective, we will intend a deeping in trichotomies of visual language as presented in matrix theory of language-thought (SANTAELLA, 2005). These trichotomies will be essential to study the controversial expressions of contemporary graphic design, in order to identify what it is innovative, which is commonplace, which transcends the current publishing paradigm and what is considered, even today, polemic by the scientific community / Esta pesquisa busca entender os mecanismos não-representativos do projeto gráfico editorial contemporâneo. O neologismo ―não-representativo‖ pretende conotar certo tipo de signo que se caracteriza pela polissemia. Na mídia impressa, esse aspecto tem insistido em despontar sob as mais variadas manifestações. Apesar de sua recorrência, esse tipo de signo não tem recebido a devida atenção por parte da comunidade científica, especialmente no que diz respeito à teoria dos signos instrumento que nos parece privilegiado para explicar as funções de linguagem ali presentes. Taxados de ilegíveis e disfuncionais, os projetos gráficos de David Carson, Neville Brody, Edward Fella, April Greiman e tantos outros são, ainda hoje, motivo de discórdia. Para ser mais específico, pode-se dizer que toda a vertente vanguardista pós-ulmiana de diversas partes do mundo questiona a racionalidade de uma área tão próxima das artes e representa uma espécie de contraponto à abordagem canônica, que desde o construtivismo e a Bauhaus tenta sistematizar uma disciplinaridade exclusivista para o design. Este contraponto ganha voz especialmente na Europa (HOLLIS, 2001) e nos EUA (MCCOY, 1990), em cujo movimento new wave tem sua representação mais característica. Um dos teóricos que trabalha com a evolução do lema modernista form follows function, Bürdek apresenta o problema da função sob um novo prisma, não mais como função exclusivamente prática, mas, principalmente, naquilo que denominou funções de signo. Segundo o autor, estas são as funções mais importantes para o design (BÜRDEK, 2002). A partir disto, busca-se responder como estas funções de signo se articulam na visualidade do projeto pós-moderno, a partir da década de 1990, para a construção de processos comunicativos que dialogam com a cultura da informação, ou com a cultura em que a função de signo supera a função de uso (BAUDRILLARD, 1995). Diferentemente da concepção estruturalista do signo em Baudrillard, entende-se por função de signo, neste estudo, os processos que fundamentam o signo segundo a semiótica peirceana (sob aspectos de qualidade, existência e regularidade). A partir dessa perspectiva, buscar-se-á um aprofundamento nas tricotomias da linguagem visual tal como apresentadas na teoria das matrizes da linguagem-pensamento (SANTAELLA, 2005). Estas tricotomias serão fundamentais para estudar as controversas expressões do design gráfico contemporâneo, com o objetivo de identificar o que nela é inovador, o que é lugar-comum, o que transcende o paradigma editorial vigente e o que nela é considerado, ainda hoje, polêmico pela comunidade científica