DocumentCode :
3175789
Title :
A new approach to numerical algorithms in terms of integrable systems
Author :
Nakamura, Yoshimasa
Author_Institution :
Dept. of Appl. Math. & Phys., Kyoto Univ., Japan
fYear :
2004
fDate :
1-2 March 2004
Firstpage :
194
Lastpage :
205
Abstract :
Almost four decades passed after the discovery of solitons and infinite dimensional integrable systems. The theory of integrable systems has had great impact to wide area in physics and mathematics. An approach to numerical algorithms in terms of integrable systems is surveyed. Some integrable systems of Lax form describe continuous flows of efficient numerical algorithms, for example, the QR algorithm and the Jacobi algorithm. Discretizations of integrable systems in tau-function level enable us to formulate algorithms for computing continued fractions such as the qd algorithm and the discrete Schur flow. A new singular value decomposition (I-SVD) algorithm is designed by using a discrete integrable system defined by the Christoffel-Darboux identity for orthogonal polynomials.
Keywords :
integral equations; polynomials; singular value decomposition; solitons; Christoffel-Darboux identity; Jacobi algorithm; QR algorithm; discrete Schur flow; integrable system theory; numerical algorithm; orthogonal polynomials; qd algorithm; singular value decomposition algorithm; Informatics; Integral equations; Jacobian matrices; Lattices; Mathematics; Physics; Polynomials; Scattering; Singular value decomposition; Solitons;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Informatics Research for Development of Knowledge Society Infrastructure, 2004. ICKS 2004. International Conference on
Print_ISBN :
0-7695-2150-9
Type :
conf
DOI :
10.1109/ICKS.2004.1313425
Filename :
1313425
Link To Document :
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