Recent Developments in Dense Numerical Linear Algebra
نویسنده
چکیده
We survey recent developments in dense numerical linear algebra, covering linear systems, least squares problems and eigenproblems. Topics considered include the design and analysis of block, partitioned and parallel algorithms, condition number estimation, componentwise error analysis, and the computation of practical error bounds. Frequent reference is made to LAPACK, the state of the art package of Fortran software designed to solve linear algebra problems efficiently and accurately on high-performance computers.
منابع مشابه
Large Dense Numerical Linear Algebra in 1993 :
This article surveys the current state of applications of large dense numerical linear algebra and the innuence of parallel computing. Furthermore, it attempts to crystallize many important ideas that are sometimes misunderstood in the rush to write fast programs.
متن کاملNumerical Linear Algebra for Model Reduction in Control and Simulation
Model reduction is an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, etc. In the past decades many approaches have been developed for reducing the order of a given model. Often these methods have been derived in parallel in different disciplines with particular applications in mind. We will discuss some of the most ...
متن کاملLarge Numerical Linear Algebra in 1994 : The Continuing In uenceof
This note covers two aspects of the state of the art of large numerical linear algebra problems. Firstly, we look at the current records for sparse and dense linear systems and eigenvalue problems on a variety of machines. Our second subject matter is perhaps more of a question than an answer. Here we explore why network topologies of a parallel machine are hardly ever used in ways that perhaps...
متن کاملCase studies on the development of ScaLAPACK and the NAG Numerical PVM Library
In this paper we look at the development of ScaLAPACK, a software library for dense and banded numerical linear algebra, and the NAG Numerical PVM Library, which includes software for dense and sparse linear algebra, quadrature, optimization and random number generation. Both libraries are aimed at distributed memory machines, including networks of workstations. The paper concentrates on the un...
متن کاملLecture Notes on Randomized Linear Algebra
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester. These notes are unchanged, relative to the notes that have been available on my web page since then; but, in response to a number of requests, I decided to put them all together as a single file and post them on the arXiv. In ...
متن کامل