Basic concepts in numerical error analysis (suggested by linear algebra problems)

Computable backward error bounds for basic algorithms in linear algebra

Standard error estimates in numerical linear algebra are often of the form γk|R||S| where R,S are known matrices and γk := ku/(1−u) with u denoting the relative rounding error unit. Recently we showed that for a number of standard problems γk can be replaced by ku for any order of computation and without restriction on the dimension. Such problems include LUand Cholesky decomposition, triangula...

Numerical linear algebra and some problems in computational statistics

for any value of x in the interval (a, b). Chebyshev motivated his problem by investigation of limit theorems in probability theory, with some related work done even earlier by Heine. It was completely resolved by Markov; for more detailed comments and description of the related developments see Shohat and Tamarkin (1943), Akhiezer (1965) and Gautschi (1981). Here we will not describe the well ...

Local Basic Linear Algebra

We describe a subset of the level{1, level{2, and level{3 BLAS implemented for each node of the Connection Machine system CM{200. The routines, collectively called LBLAS, have interfaces consistent with languages with an array syntax such as Fortran 90. One novel feature, important for distributed memory architectures, is the capability of performing computations on multiple instances of object...

Numerical Linear Algebra and Matrix Analysis

Numerical Linear Algebra With

SUMMARY StratiGraph, a Java-based tool for computation and presentation of closure hierarchies of Jordan and Kronecker structures is presented. The tool is based on recent theoretical results on stratiications of orbits and bundles of matrices and matrix pencils. A stratiication reveals the complete hierarchy of nearby structures, information critical for explaining the qualitative behavior of ...