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Book Review
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Book Information
Author(s):
Loo Keng Hua and Yuan Wang
Title:
Applications of number theory to numerical analysis
Additional book information:
Springer-Verlag, Berlin, Science Press, Beijing, 1981, 241 pp., $39.00
References:
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- 3.
- H. Conroy, Molecular Schrödinger equation. VII: A new method for the evaluation of multidimensional integrals, J. Chem. Phys. 47 (1967), 5307-5318.
- 4.
- U. Dieter, Autokorrelation multiplikativ-erzeugter Pseudo-Zufallszahlen, Operations Research Verfahren 6 (1969), 69-85.
- 5.
- U. Dieter and J. Ahrens, An exact determination of serial correlation of pseudo-random numbers, Numer. Math 16 (1971), 101-123. MR 286245
- 6.
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- 7.
- H. Halton, On the efficiency of quasi-random sequences of points in evaluating multidimensional integral, Numer. Math. 2 (1960), 84-90. MR 121961
- 8.
- E. Hlawka, Uniform distribution modulo 1 and numerical analysis, Compositio Math. 16 (1964), 92-105. MR 175278
- 9.
- D. H. Knuth, The art of computer programming (esp. Vol. 2), Addison-Wesley, Reading, Mass., 1969.
- 10.
- Z. Kopal, Numerical analysis, Wiley, New York, 1955. MR 77213
- 11.
- N. M. Korobov, Approximate calculation of multiple integrals with the aid of methods in the theory of numbers, Dokl. Akad. Nauk SSSR 115 (1957), 1062-1065. MR 98714
- 12.
- N. M. Korobov, An approximate calculation of multiple integrals, Dokl. Akad. Nauk SSSR 124 (1959), 1207-1210. MR 104086
- 13.
- N. M. Korobov, Number-theoretic methods of approximate analysis, Fitmatgiz, Moscow, 1963.
- 14.
- L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley, 1974. MR 419394
- 15.
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- 16.
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- 17.
- W. M. Schmidt, Simultaneous approximation of algebraic numbers by rationals, Acta Math. 125 (1970), 189-201. MR 268129
- 18.
- W. M. Schmidt, Diophantine approximations, Lecture Notes in Math., vol. 785, Springer-Verlag, Berlin, and New York, 1980. MR 568710
- 19.
- S. K. Zaremba, Good lattice points, discrepancy and numerical integration, Ann. Mat. Pura Appl. 73 (1966), 293-317. MR 218018
- 20.
- S. K. Zaremba, La discrépance isotope et l'intégration numérique, Ann. Mat. Pura Appl. 87 (1970), 125-136.
- 21.
- S. K. Zaremba, La méthode des "bons tréillis" pour le calcul des intégrales multiples, see [23, pp. 39-116]. MR 343530
- 22.
- S. K. Zaremba, Some applications of multidimensional integration by parts, Ann. Polon. Math. 21 (1968), 85-96. MR 235731
- 23.
- S. K. Zaremba, (Editor), Applications of number theory to numerical analysis, Academic Press, New York, 1972. MR 334452
Additional Information:
Reviewer(s):
Emil
Grosswald
Review Information:
Journal:
Bull. Amer. Math. Soc.
8
(1983),
489-496.
DOI:
10.1090/S0273-0979-1983-15132-7
PII:
S 0273-0979(1983)15132-7
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