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Methods of numerical integration. 2nd ed. (English) Zbl 0537.65020
Computer Science and Applied Mathematics. Orlando etc.: Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers). XIV, 612 p. $ 52.00; £36.50 (1984).
This is the second edition of the well-known book on numerical integration [for the first edition from 1975 see Zbl 0304.65016]. The basic difference between the first and the second edition is that some new material is given on approximate integration in \(R^ n\), \(n\geq 2\), and on automatic integration, and the bibliography is updated. The plan and the objectives of the book remain the same. The authors mention that the new results on optimal quadratures (especially on cubatures), and the work of the Soviet school are not well represented in the book. There are several books on this subject [see V. I. Krylov, Approximate calculation of integrals (1959; Zbl 0086.329), I. M. Sobol’, Cubatures and Haar’s functions (1969; Zbl 0195.169), V. I. Krylov and L. T. Shul’gina, Reference book on numerical integration (1966; Zbl 0152.151), S. L. Sobolev, Introduction into the theory of cubatures, ibid. (1974; Zbl 0294.65013), A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall, Englewood Cliffs (1971; Zbl 0379.65013) and I. Mysovskikh, Interpolational cubature formulas (1981; reviewed above)]. The books by I. Sobol’ and I. Mysovskikh are not mentioned in the bibliography, and many results in these two books and in the book by Sobolev are not represented. The book will be useful for many people in applied mathematics and numerical analysis.
Reviewer: A.G.Ramm

65D32 Numerical quadrature and cubature formulas
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65D30 Numerical integration
41A55 Approximate quadratures
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)