tailieunhanh - Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 158

Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 158', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 606 Chapter 13. Fourier and Spectral Applications to near neighbors in its own hierarchy square blocks along the main diagonal and near neighbors in other hierarchies rectangular blocks off the diagonal . The number of nonnegligible elements in a matrix like that in Figure scales only as N the linear size of the matrix as a rough rule of thumb it is about 10Nlog10 1 e where e is the truncation level . 10 6. For a 2000 by 2000 matrix then the matrix is sparse by a factor on the order of 30. Various numerical schemes can be used to solve sparse linear systems of this hierarchically band diagonal form. Beylkin Coifman and Rokhlin 1 make the interesting observations that 1 the product of two such matrices is itself hierarchically band diagonal truncating of course newly generated elements that are smaller than the predetermined threshold e and moreover that 2 the product can be formed in order N operations. Fast matrix multiplication makes it possible to find the matrix inverse by Schultz s or Hotelling s method see . Other schemes are also possible for fast solution of hierarchically band diagonal forms. For example one can use the conjugate gradient method implemented in as linbcg. CITED REFERENCES AND FURTHER READING Daubechies I. 1992 Wavelets Philadelphia . . Strang G. 1989 SIAM Review vol. 31 pp. 614-627. Beylkin G. Coifman R. and Rokhlin V. 1991 Communications on Pure and Applied Mathematics vol. 44 pp. 141-183. 1 Daubechies I. 1988 Communications on Pure andApplied Mathematics vol. 41 pp. 909-996. 2 Vaidyanathan . 1990 Proceedings of the IEEE vol. 78 pp. 56-93. 3 Mallat . 1989 IEEE Transactions on Pattern Analysis and Machine Intelligence vol. 11 pp. 674-693. 4 Freedman . and Press . 1992 preprint. 5 Numerical Use ofthe Sampling Theorem In we implemented an approximating formula for Dawson s integral due to Rybicki. Now that we have become Fourier sophisticates we can learn that the formula derives from numerical

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