Abstract: The chapter discusses the special difficulties of linear approximation in several variables. The first setback occurs with the discovery that there are no Chebyshev sets in many dimensions; therefore, minimax approximation is not necessarily unique. Linear interpolation is not always feasible; this is especially awkward as it is the obvious symmetrical arrangements of points that are most liable to give trouble. The chapter also discusses the common problem of evaluation over some region of a multiple integral. The principal methods in common use fall into three categories: (1) Cartesian-product methods; (2) efficient methods, which are in principle extensions of Gauss formulae to regions of higher dimensionality, designed to integrate exactly all polynomials of a given total degree using the fewest possible function values; and (3) Monte Carlo methods.
Publication Year: 1966
Publication Date: 1966-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 5
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