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Orthogonality — Conventional and Unconventional — In Numerical Analysis

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Computation and Control

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 1))

Abstract

The idea of orthogonality is widespread in numerical analysis. In its analytic form, it is used to great advantage in problems of least squares approximation, quadrature, and differential equations. The principal tools are orthogonal polynomials. In its algebraic (finite-dimensional) form, orthogonality underlies many iterative methods for solving large systems of linear algebraic equations. If used in similarity transformations, it leads to effective methods of computing eigenvalues. Here, we shall limit ourselves to two application areas: numerical quadrature and univariate approximation. We review a number of applications in which orthogonality plays a significant role and in some of which nonstandard features suggest interesting new problems of analysis and computation.

Work supported, in part, by the National Science Foundation under grant CCR-8704404.

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Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, West Lafayette, IN, 47907, USA

    Walter Gautschi

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© 1989 Birkhäuser Boston

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Gautschi, W. (1989). Orthogonality — Conventional and Unconventional — In Numerical Analysis. In: Computation and Control. Progress in Systems and Control Theory, vol 1. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3704-4_5

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  • DOI: https://doi.org/10.1007/978-1-4612-3704-4_5

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3438-4

  • Online ISBN: 978-1-4612-3704-4

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