Applications of number theory to numerical analysis / Loo Keng Hua, Yuan Wang
Language: English
Published by Berlin, Heidelberg : Springer-Verlag, 1981
- First Edition
- Hardcover
- Used
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Fine copy in the original colour-printed boards. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; X, 244 pp. Notes; Includes bibliographical references and index. Contents; 1. Algebraic Number Fields and Rational Approximation -- §1.1. The units of algebraic number fields -- §1.2. The simultaneous Biophantine approximation of an integral basis -- §1.3. The real eyelotomie field -- §1.4. The units of a eyelotomie field -- §1.5. Continuation -- §1.6. The Drriehlet field -- §1.7. The cubic field -- Notes -- 2. Recurrence Relations and Rational Approximation -- §2.1. The recurrence formula for the elementary symmetric fonction -- §2.2. The generalization of Sn -- §2.3. PV numbers -- § 2.4. The roots of the equation F(x) = 0 -- §2.5. The roots of the equation G(x) = 0 -- §2.6. The roots of the equation E(x) = 0 -- §2.7. The irreducibility of a polynomial -- §2.8. The rational approximations of ?, ?, ? -- Notes -- 3. Uniform Distribution -- §3.1. Uniform distribution -- §3.2. Vinogradov’s lemma -- §3.3. The exponential sum and the discrepancy -- §3.4. The number of solutions to the congruence -- §3.5. The solutions of the congruence and the discrepancy -- §3.6. The partial summation formula -- §3.7. The comparison of discrepancies -- §3.8. Eational approximation and the solutions of the congruence -- §3.9. The rational approximation and the discrepancy -- §3.10. The lower estimate of discrepancy -- Notes -- 4. Estimation of Discrepancy -- §4.1. The set of equi-distribution -- §4.2. The Halton theorem -- §4.3. The p set -- §4.4. The gp set -- §4.5. The eonstruetion of good points -- §4.6. The ?s set -- §4.7. The ? set -- §4.8. The ease s = 2 -- §4.9. The glp set -- Notes -- 5. Uniform Distribution and Numerical Integration -- §5.1. The function of bounded variation -- §5.2. Uniform distribution and numerical integration -- §5.3. The lower estimation for the error term of quadrature formula -- §5.4. The quadrature formulas -- Notes -- 6. Periodic Functions -- §6.1. The classes of functions -- §6.2. Several lemmas -- §6.3. The relations between Hs?(C), Qs?(C) and Es?(C) -- §6.4. Periodic functions -- § 6.5. Continuation -- Notes -- 7. Numerical Integration of Periodic Functions -- §7.1. The set of equi-distribution and numerical integration -- §7.2. The p set and numerical integration -- §7.3. The gp set and numerical integration -- §7.4. The lower estimation of the error term for the quadrature formula -- §7.5. The solutions of congruences and numerical integration -- §7.6. The glp set and numerical integration -- §7.7. The Sarygin theorem -- §7.8. The mean error of the quadrature formula -- §7.9. Continuation -- Notes -- 8. Numerical Error for Quadrature Formula -- §8.1. The numerical error -- §8.2. The comparison of good points -- §8.3. The computation of the ? set -- §8.4. The computation of the ?s set -- §8.5. Examples of other F s sets -- §8.6. The computation of a glp set -- §8.7. Several remarks -- §8.8. Tables -- § 8.9. Some examples -- Notes -- 9. Interpolation -- §9.1. Introduction -- §9.2. The set of equi-distribution and interpolation -- §9.3. Several lemmas -- §9.4. The approximate formula of the function of E?s(C) -- §9.5. The approximate formula of the function of Q?s(C) -- §9.6. The Bernoulli polynomial and the approximate polynomial -- §9.7. The ? results -- Notes -- 10. Approximate Solution of Integral Equations and Differential Equations -- §10.1. Several lemmas -- § 10.2. The approximate solution of the Fredholm integral equation of second type -- § 10.3. The approximate solution of the Volterra integral equation of second type -- §10.4. The eigenvalue and eigenfunction of the Fredholm equation -- § 10.5. The Cauehy problem of the partial differential equation of the parabolic type -- § 10.6. The Diriehlet problem of the partial differential equation of the elliptic type -- § 10.7. Several remarks -- Notes -- Appendix Tables. Subjects; Numerical analysis. Arithmeti. …
Seller Inventory # 385173
- Title
- Applications of number theory to numerical analysis / Loo Keng Hua, Yuan Wang
- Author
- Hua, Luogeng (1910-1985)
- Publisher
- Berlin, Heidelberg : Springer-Verlag
- Publication year
- 1981
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 3540103821
- ISBN 13
- 9783540103820
- Edition
- 1st edition.
- Item weight
- 1 kilogram
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