Householder triangularization of a quasimatrix

A standard algorithm for computing the QR factorization of a matrix A is Householder triangularization. Here this idea is generalized to the situation in which A is a quasimatrix, that is, a “matrix” whose “columns” are functions defined on an interval [a,b]. Applications are mentioned to quasimatrix leastsquares fitting, singular value decomposition, and determination of ranks, norms, and condition numbers, and numerical illustrations are presented using the chebfun system

Parallel bidiagonalization of a dense matrix

A new stable method for the reduction of rectangular dense matrices to bidiagonal form has been proposed recently. This is a one-sided method since it can be entirely expressed in terms of operations with (full) columns of the matrix under transformation. The algorithm is well suited to parallel computing and, in order to make it even more attractive for distributed memory systems, we introduce a modification which halves the number of communication instances. In this paper we present such a modification. A block organization of the algorithm to use level~3 BLAS routines seems difficult and, at least for the moment, it relies upon level~2 BLAS routines. Nevertheless, we found that our sequential code is competitive with the LAPACK DGEBRD routine. We also compare the time taken by our parallel codes and the ScaLAPACK PDGEBRD routine. We investigated the best data distribution schemes for the different codes and we can state that our parallel codes are also competitive with the ScaLAPACK routine.Fundação para a Ciência e a Tecnologia (FCT) - programa POCI 2010

Модель и программная реализация сингулярного оценивания частоты основного тона речевого сигнала

The article deals with software implementation of the evaluation of the pitch frequency of the speech signal based on the mathematical apparatus for singular spectral analysis. The program is used in calculation module of a program complex for speech rehabilitation of cancer patients after resection of larynx used in rehabilitation training of patients after complete or partial loss of sounding speech as a result of laryngectomy.В статье рассматривается сингулярная модель оценивания частоты основного тона речевого сигнала, а также ее программная реализация. Применение модели сингулярного оценивания частоты основного тона позволяет уменьшить вычислительную сложность алгоритмов анализа речевого сигнала путем аппроксимации края сингулярного спектра и обеспечить меньшее количество ошибок оценивания частоты основного тона за счет использования сингулярной модели вокализированного сегмента речи, учитывающей нестационарные параметры основного тона с помощью собственных чисел. Программная реализация модели используется в модуле расчетов комплекса программ речевой реабилитации онкологических больных после резекции гортани. Ключевые слова: оценивание частоты основного тона речевого сигнала, сингулярный спектральный анализ речи, модель, программная реализация

Hacia la optimización de un sistema de recuperación de información

Con el desarrollo de los repositorios digitales cada vez ha cobrado mayor interés el estudio de los Sistemas de Recuperación de Información. El volumen de la información contenida en dichos repositorios crece de forma exponencial con lo cual búsqueda de los documentos que respondan a la necesidad de los usuarios se torna una tarea difícil. En este contexto este grupo de investigación ha estado trabajando por más de ocho años en la construcción de sus propios motores de búsqueda y recuperación orientados a corpus estáticos. Una vez construidos dichos motores las líneas de investigación se han orientado a distintos enfoques que pretenden acelerar los mismos tanto en la búsqueda como en los preprocesos. En particular, en esta etapa se tiene por objetivo la investigación, desarrollo e implementación de algoritmos paralelos, principalmente para resolver el proceso de la de Descomposición en Valores Singulares en arquitecturas basadas en Unidades de Procesamiento Gráfico y su comparación con clústeres de multicores, así como el empleo de soluciones híbridas que combinen ambos enfoques.Eje: Procesamiento distribuido y paralelo.Red de Universidades con Carreras en Informátic

Comparación de un algoritmo de bidiagonalización para su utilización en la recuperación de información

Este artículo presenta parte del trabajo realizado en el marco de una investigación que pretende optimizar un Sistema de Recuperación de Información, mediante la implementación y evaluación de distintos algoritmos secuenciales y paralelos para resolver eficientemente la Descomposición en Valores Singulares. Tal proceso comienza con llevar la matriz inicial a la forma bidiagonal, lo que puede consumir más del 70% del tiempo total del proceso. Por ello, como trabajo preliminar se han estudiado distintos métodos de bidiagonalización. Este trabajo se relaciona al desarrollo e implementación de un algoritmo de bidiagonalización alternativo para comparar posteriormente su comportamiento en distintas arquitecturas, en particular, las basadas en unidades de procesamiento gráfico, monoprocesadores y multiprocesadores. La experiencia de este estudio concreto ha permitido un análisis de rendimiento al ejecutar el algoritmo en cada implementación, cuando se varía el tamaño de las matrices, identificando problemas mínimos en GPU en cuanto a diferencias en la precisión de datos.Workshop: WPDP – Procesamiento Distribuido y ParaleloRed de Universidades con Carreras en Informátic

On rigid origami III: local rigidity analysis.

In this article, rigid origami is examined from the perspective of rigidity theory. First- and second-order rigidity are defined from local differential analysis of the consistency constraint; while the static rigidity and prestress stability are defined after finding the form of internal force and load. We will show the hierarchical relation among these local rigidities with examples representing different levels. The development of theory here follows the same path as the conventional rigidity theory for bar-joint frameworks, but starts with different high-order rotational constraints. We also bring new interpretation to the internal force and geometric error of constraints associated with energy. Examining the different aspects of the rigidity of origami might give a novel perspective for the development of new folding patterns, or for the design of origami structures where some rigidity is required

On rigid origami III: local rigidity analysis.

In this article, rigid origami is examined from the perspective of rigidity theory. First- and second-order rigidity are defined from local differential analysis of the consistency constraint; while the static rigidity and prestress stability are defined after finding the form of internal force and load. We will show the hierarchical relation among these local rigidities with examples representing different levels. The development of theory here follows the same path as the conventional rigidity theory for bar-joint frameworks, but starts with different high-order rotational constraints. We also bring new interpretation to the internal force and geometric error of constraints associated with energy. Examining the different aspects of the rigidity of origami might give a novel perspective for the development of new folding patterns, or for the design of origami structures where some rigidity is required

Robust parametric modeling of speech in additive white Gaussian noise

ABSTRACT: In estimating the linear prediction coefficients for an autoregressive spectral model, the concept of using the Yule-Walker equations is often invoked. In case of additive white Gaussian noise (AWGN), a typical parameter compensation method involves using a minimal set of Yule-Walker equation evaluations and removing a noise variance estimate from the principal diagonal of the autocorrelation matrix. Due to a potential over-subtraction of the noise variance, however, this method may not retain the symmetric Toeplitz structure of the autocorrelation matrix and there- by may not guarantee a positive-definite matrix estimate. As a result, a significant decrease in es- timation performance may occur. To counteract this problem, a parametric modelling of speech contaminated by AWGN, assuming that the noise variance can be estimated, is herein presented. It is shown that by combining a suitable noise variance estimator with an efficient iterative scheme, a significant improvement in modelling performance can be achieved. The noise variance is esti- mated from the least squares analysis of an overdetermined set of p lower-order Yule-Walker eq- uations. Simulation results indicate that the proposed method provides better parameter estimates in comparison to the standard Least Mean Squares (LMS) technique which uses a minimal set of evaluations for determining the spectral parameters