By S.K. Zaremba

ISBN-10: 0127759506

ISBN-13: 9780127759500

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**Extra resources for Applications of Number Theory to Numerical Analysis**

**Sample text**

P. s of the form ford us sequences that have exponent s-1, which is the best that may be possible, for for each a. Comparison of the next to last columns of Tables IV, VI, and VII with those of Tables I, II, and III respectively indicates that if the error bound Β is indeed for both the Hua-Wang and the restricted M Korobov sequences, the constants implied in the <9" are much smaller for the latter sequences. This makes them more useful for numerical integration, of course. It should be noted that while the present calculations were done to investigate the asymptotic behavior of certain sequences of quadrature formulas, they have also produced a large number of actual quadrature formulas together with error bounds for them.

25 103. SEYMOUR HABER Example 3: k2 s = 5, k = 9,389; k = 6,408, fe3 = 2,908, k^ = 7,800. 0669. Example 4: k2 s = 6, k = 41,204; k^ = 33,810, = 31,766, k^ = 20,480, & 4 = 5,610, k^ = 29,223. 110. Example 5: k2 s = 11, k = 698,047; ^ = 685,041, = 646,274, & 3 = 582,461, k^ = 494,796, fe5 = 384,914, k^ = 254,860, kn = 107,051, fc0 = 642,292, k„ = 467,527, = 284,044. 0. M. KOROBOV, On approximate calculation of multiple integrals (Russian), Dokl. Akad. Nauk SSSR 124 (1959), 1207-1210. M. KOROBOV, Numb er-The ore tic Methods of Approximate Analysis (Russian), [3] Fizmatgiz, Moscow, 1963.

0371. 25 103. SEYMOUR HABER Example 3: k2 s = 5, k = 9,389; k = 6,408, fe3 = 2,908, k^ = 7,800. 0669. Example 4: k2 s = 6, k = 41,204; k^ = 33,810, = 31,766, k^ = 20,480, & 4 = 5,610, k^ = 29,223. 110. Example 5: k2 s = 11, k = 698,047; ^ = 685,041, = 646,274, & 3 = 582,461, k^ = 494,796, fe5 = 384,914, k^ = 254,860, kn = 107,051, fc0 = 642,292, k„ = 467,527, = 284,044. 0. M. KOROBOV, On approximate calculation of multiple integrals (Russian), Dokl. Akad. Nauk SSSR 124 (1959), 1207-1210. M. KOROBOV, Numb er-The ore tic Methods of Approximate Analysis (Russian), [3] Fizmatgiz, Moscow, 1963.

### Applications of Number Theory to Numerical Analysis by S.K. Zaremba

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