Schur flow for orthogonal polynomials on the unit circle and its integrable discretization

Journal of Computational and Applied Mathematics

Volumn 139, Issue 1, 2002, Pages 75-94

  Mukaihira, Atsushi ^a   Nakamura, Yoshimasa ^b,c  

^a MITSUBISHI RESEARCH INSTITUTE   (Japan)

^b OSAKA UNIVERSITY   (Japan)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

Integrable discretization; Orthogonal polynomials on the unit circle; Pad approximation; Perron Carath odory continued fraction; Schur flow

Indexed keywords

INTEGRAL EQUATIONS; PARAMETER ESTIMATION; POLYNOMIAL APPROXIMATION;

SCHUR FLOW;

POLYNOMIALS;

MATHEMATICAL ANALYSIS;

EID: 0036467696     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(01)00388-0     Document Type: Article

References (28)

1. Nonlinear differential-difference equations and fourier analysis
2. Schur flows for orthogonal Hessenberg matrices
3. Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation
4. The integration of semi-infinite Toda chain by means of inverse spectral problem
5. Reduced unitary matrix models and the hierarchy of ζ-functions
6. The half-infinite discretized Hirota equation and the trigonometric moment problem
7. Inverse problems for orthogonal matrices, Toda flows, and signal processing
8. On Schur flows
9. Accurate singular values and differential qd algorithms
10. Difference scheme of soliton equations
11. Continued fractions in numerical analysis
12. On an explicitly soluble system of nonlinear differential equations related to certain Toda lattice
13. Orthogonal polynomials and the finite Toda lattice
14. Complete integrability and stochastization of discrete dynamical systems
15. Korteweg-de Vries equation and generalization I. A remarkable explicit nonlinear transformation
16. Finitely many mass points on the line under the influence of an exponential potential - An integrable system
17. Calculating laplace transforms in terms of the Toda molecule
18. On an integrable discretization of the Rayleigh quotient gradient system and the power method with a shift
19. Moment problem of Hamburger, hierarchies of integrable systems, and the positivity of tau-functions
20. Unitary-matrix models as exactly solvable string theories
21. Time-dependent orthogonal polynomials and theory of soliton - Applications to matrix model, vertex model and level statistics
22. Conserved quantities of nonlinear difference equations