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The interplay between classical analysis and (numerical) linear algebra – a tribute to Gene H. Golub. (English) Zbl 1065.65049

Summary: 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.

MSC:

65F10 Iterative numerical methods for linear systems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65D32 Numerical quadrature and cubature formulas
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
15A45 Miscellaneous inequalities involving matrices
65F20 Numerical solutions to overdetermined systems, pseudoinverses

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