Volume 13, pp. 119-147, 2002.

The interplay between classical analysis and (numerical) linear algebra - a tribute to Gene H. Golub

Walter Gautschi

Abstract

Much of the work of Golub and his collaborators uses techniques of linear algebra to deal with problems in analysis, or employs tools from analysis to solve problems arising in linear algebra. Instances are described of such interdisciplinary work, taken from quadrature theory, orthogonal polynomials, and least squares problems on the one hand, and error analysis for linear algebraic systems, element-wise bounds for the inverse of matrices, and eigenvalue estimates on the other hand.

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Key words

Gauss-type quadratures, eigenvalue/vector characterizations, orthogonal polynomials, modification algorithms, polynomials orthogonal on several intervals, least squares problem, Lanczos algorithm, bounds for matrix functionals, iterative methods.

AMS subject classifications

65D32, 33C45, 65D10, 15A45, 65F10.

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