Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...

Alan J. Laub Using an approach that its author calls “matrix analysis for grown-ups,” this new textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It provides readers with a one-semester introduction to numerical linear algebra; an introduction to statistical condition...

An attractive paradigm for building fast numerical algorithms is the following: (1) try a fast but occasionally unstable algorithm, (2) test the accuracy of the computed answer, and (3) recompute the answer slowly and accurately in the unlikely event it is necessary. This is especially attractive on parallel machines where the fastest algorithms may be less stable than the best serial algorithm...

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.

We provide a real algebraic symbolic-numeric algorithm for computing the real variety VR(I) of an ideal I ⊆ R[x], assuming VR(I) is finite (while VC(I) could be infinite). Our approach uses sets of linear functionals on R[x], vanishing on a given set of polynomials generating I and their prolongations up to a given degree, as well as on polynomials of the real radical ideal R √ I obtained from ...

We present fast and numerically stable algorithms for the solution of linear systems of equations, where the coefficient matrix can be written in the form of a banded plus semiseparable matrix. Such matrices include banded matrices, banded bordered matrices, semiseparable matrices, and block-diagonal plus semiseparable matrices as special cases. Our algorithms are based on novel matrix factoriz...

We are interested in the solution of incompressible ows possessing densities that vary both discontinuously and smoothly. Smooth density variations might be caused by temperature eeects, whereas abrupt variations are present at immiscible uid interfaces. If interfaces are present, we wish to model their gross topological changes. The design of an incom-pressible ow algorithm that maintains solu...

In this paper, the ident(fitzahm probl~n, the tolermu:e probl~n, and the amtrol problon are treated for the interval linear equation A z = b. These problems require computing ;in inner approximatiem of the unitM .~h,ion. sa E s ~ ( A , b) = {x E R n I (3A ~ A ) ( A x ~ b ) } , f the tolerable sohaion .~et ~vS(A, b ) = {x R '~ ] (VA E A ) ( A x ~ b)} , and of the cmmoltabte.~dtaion.*a E ~ v ( A ...

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...