7 research outputs found
Perturbation splitting for more accurate eigenvalues
Let be a symmetric tridiagonal matrix with entries and
eigenvalues of different magnitudes. For some , small entrywise
relative perturbations induce small errors in the eigenvalues,
independently of the size of the entries of the matrix; this is
certainly true when the perturbed matrix can be written as
with small . Even if it is
not possible to express in this way the perturbations in every
entry of , much can be gained by doing so for as many as
possible entries of larger magnitude. We propose a technique which
consists of splitting multiplicative and additive perturbations
to produce new error bounds which, for some matrices, are much
sharper than the usual ones. Such bounds may be useful in the
development of improved software for the tridiagonal eigenvalue
problem, and we describe their role in the context of a mixed
precision bisection-like procedure. Using the very same idea of
splitting perturbations (multiplicative and additive), we show
that when defines well its eigenvalues, the numerical values
of the pivots in the usual decomposition may
be used to compute approximations with high relative precision.Fundação para a Ciência e Tecnologia (FCT) - POCI 201
Quantitative performance modeling of scientific computations and creating locality in numerical algorithms
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 141-150) and index.by Sivan Avraham Toledo.Ph.D
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described