Abstract
The univariate qd-algorithm is very useful for the determination of poles of meromorphic functions and eigenvalues of certain tridiagonal matrices. Both applications are linked to the theory of orthogonal polynomials, in particular the formally orthogonal Hadamard polynomials.
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References
Benouahmane, B. and Cuyt, A. (1999): Properties of multivariate homogeneous orthogonal polynomials. J. Approx. Th. submitted.
Benouahmane, B., Cuyt, A. and Verdonk, B. (2000): On the solution of parameterized (smallest) eigenvalue problems. SIAM J. Matrix Anal. & Applcs. submitted.
Brezinski, C. (1980): Padé type approximation and general orthogonal polynomials. Birkhauser Verlag, Basel.
Chaffy, C. (1984): Interpolation polynomiale et rationnelle d’une fonction de plusieurs variables complexes. Thèse. Inst. Polytech., Grenoble.
Cuyt, A. (1988): A multivariate qd-like algorithm. BIT 28: 98–112.
Cuyt, A. (1992): Extension of “A multivariate convergence theorem of the de Montessus de Ballore type” to multipoles. J. Comput. Appl. Math.41: 323–330.
Cuyt, A. (1994): On the convergence of the multivariate “homogeneous” qd-algorithm. BIT 34: 535–545.
Cuyt, A. and Verdonk, B. (1999): Extending the qd-algorithm to tackle multivariate problems. In: Papamichael, N., Ruscheweyh, S., and Saff, B. (eds.): Proceedings of the Third CMFT Conference “Computational methods and function theory 1997“, Nicosia, Cyprus. World Scientific, pp. 135–159.
Fernando, K. and Parlett, B. (1994): Accurate singular values and differential qd algorithms. Numer. Math. 67: 191–229.
Henrici, P. (1974): Applied and computational complex analysis I. John Wiley, New York.
Von Matt, U. (1997): The orthogonal QD-algorithm. SIAM J. Sci. Statist. Comput. 18: 1163–1186.
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Cuyt, A. (2001). Symbolic-Numeric QD-algorithms with applications in Function theory and Linear algebra. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6280-4_5
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DOI: https://doi.org/10.1007/978-3-7091-6280-4_5
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