Book Review
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MathSciNet review:
1567432
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Book Information:
Authors:
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.
A. Baker, On some Diophantine inequalities involving the exponential function, Canadian J. Math. 17 (1965), 616–626. MR 177946, DOI 10.4153/CJM-1965-061-8
Heinrich P. Baltes, Peter K. J. Draxl, and Eberhard R. Hilf, Quadratsummen und gewisse Randwertprobleme der mathematischen Physik, J. Reine Angew. Math. 268(269) (1974), 410–417 (German). MR 344210
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.
U. Dieter and J. Ahrens, An exact determination of serial correlations of pseudorandom numbers, Numer. Math. 17 (1971), 101–123. MR 286245, DOI 10.1007/BF01406000
Seymour Haber, Experiments on optimal coefficients, Applications of number theory to numerical analysis (Proc. Sympos., Univ. Montréal, Montreal, Que., 1971) Academic Press, New York, 1972, pp. 11–37. MR 0391479
J. H. Halton, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math. 2 (1960), 84–90. MR 121961, DOI 10.1007/BF01386213
Edmund Hlawka, Uniform distribution modulo $1$ and numerical analysis, Compositio Math. 16 (1964), 92–105 (1964). MR 175278
9. D. H. Knuth, The art of computer programming (esp. Vol. 2), Addison-Wesley, Reading, Mass., 1969.
Zdeněk Kopal, Numerical analysis. With emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable, John Wiley & Sons, Inc., New York, 1955. MR 0077213
N. M. Korobov, Approximate calculation of repeated integrals by number-theoretical methods, Dokl. Akad. Nauk SSSR (N.S.) 115 (1957), 1062–1065 (Russian). MR 0098714
N. M. Korobov, Approximate evaluation of repeated integrals, Dokl. Akad. Nauk SSSR 124 (1959), 1207–1210 (Russian). MR 0104086
13. N. M. Korobov, Number-theoretic methods of approximate analysis, Fitmatgiz, Moscow, 1963.
L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0419394
D. H. Lehmer, Mathematical methods in large-scale computing units, Proceedings of a Second Symposium on Large-Scale Digital Calculating Machinery, 1949, Harvard University Press, Cambridge, Mass., 1951, pp. 141–146. MR 0044899
Kaj L. Nielsen, Methods in numerical analysis, The Macmillan Company, New York, 1956. MR 0076428
Wolfgang M. Schmidt, Simultaneous approximation to algebraic numbers by rationals, Acta Math. 125 (1970), 189–201. MR 268129, DOI 10.1007/BF02392334
Wolfgang M. Schmidt, Diophantine approximation, Lecture Notes in Mathematics, vol. 785, Springer, Berlin, 1980. MR 568710
S. C. Zaremba, Good lattice points, discrepancy, and numerical integration, Ann. Mat. Pura Appl. (4) 73 (1966), 293–317. MR 218018, DOI 10.1007/BF02415091
20. S. K. Zaremba, La discrépance isotope et l'intégration numérique, Ann. Mat. Pura Appl. 87 (1970), 125-136.
S. K. Zaremba, La méthode des “bons treillis” pour le calcul des intégrales multiples, Applications of number theory to numerical analysis (Proc. Sympos., Univ. Montréal, Montreal, Que., 1971) Academic Press, New York, 1972, pp. 39–119 (French, with English summary). MR 0343530
S. C. Zaremba, Some applications of multidimensional integration by parts, Ann. Polon. Math. 21 (1968), 85–96. MR 235731, DOI 10.4064/ap-21-1-85-96
S. K. Zaremba (ed.), Applications of number theory to numerical analysis, Academic Press, New York-London, 1972. MR 0334452
- 1.
- A Baker, On some Diophantine inequalities involving exponential functions, Canad. J. Math. 17 (1965), 616-626. MR 0177946
- 2.
- H. Baltes, P. K. Draxl and E. R. Hilf, Quadratsummen und gewisse Randwertprobleme der mathematischen Physik, J. Reine Angew. Math. 268/269 (1974), 410-417. MR 344210
- 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.
- S. Haber, Experiments in coefficients, see [23, pp. 11-37]. MR 391479
- 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.
- D. H. Lehmer, Mathematical methods in large-scale computing units, Proc. Second Sympos. on Large-Scale Digital Calcul. Machinery, Harvard Univ. Press, Cambridge, Mass., 1949, pp. 141-146. MR 44899
- 16.
- K. J. Nielson, Methods in numerical analysis, Macmillan, New York, 1956. MR 76428
- 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
Review Information:
Reviewer:
Emil Grosswald
Journal:
Bull. Amer. Math. Soc.
8 (1983), 489-496
DOI:
https://doi.org/10.1090/S0273-0979-1983-15132-7
