Self-adapting software for numerical linear algebra and LAPACK for clusters

Self Adapting Software for Numerical Linear Algebra and LAPACK for Clusters

Computation of a canonical form for linear differential-algebraic equations

This paper describes how a commonly used canonical form for linear differential-algebraic equations can be computed using numerical software from the linear algebra package LAPACK. This makes it possible to automate for example observer construction and parameter estimation in linear models generated by a modeling language like Modelica.

Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem

Elementary plane rotations are one of the building blocks of numerical linear algebra and are employed in reducing matrices to condensed form for eigenvalue computations and during the QR algorithm. Unfortunately, their implementation in standard packages such as EISPACK, the BLAS and LAPACK lack the continuity of their mathematical formulation, which makes results from software that use them s...

Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0)

The SDPA (SemiDefinite Programming Algorithm) is a software package for solving general SDPs (SemiDefinite Programs). It is written in C++ with the help of LAPACK for numerical linear algebra for dense matrix computation. The purpose of this paper is to present a brief description of the latest version of the SDPA and its high performance for large scale problems through numerical experiment an...

Testing linear algebra software

How can we test the correctness of a computer implementation of an algorithm such as Gaussian elimination, or the QR algorithm for the eigenproblem? This is an important question for program libraries such as LAPACK, that are designed to run on a wide range of systems. We discuss testing based on verifying known backward or forward error properties of the algorithms, with particular reference t...