Gautschi, Walter The interplay between classical analysis and (numerical) linear algebra – a tribute to Gene H. Golub. (English) Zbl 1065.65049 ETNA, Electron. Trans. Numer. Anal. 13, 119-147 (2002). 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. Cited in 33 Documents 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 Keywords: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 Software:QUADPACK PDFBibTeX XMLCite \textit{W. Gautschi}, ETNA, Electron. Trans. Numer. Anal. 13, 119--147 (2002; Zbl 1065.65049) Full Text: EuDML EMIS