On orthogonal polynomials of Sobolev type: algebraic properties and zeros
SIAM Journal on Mathematical Analysis
Results on the associated Jacobi and Gegenbauer polynomials
SPOA VII Proceedings of the seventh Spanish symposium on Orthogonal polynomials and applications
On recurrence relations for Sobolev orthogonal polynomials
SIAM Journal on Mathematical Analysis
Recurrence relations for connection coefficients between two families of orthogonal polynomials
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Fourth-order difference equation for the associated classical discrete orthogonal polynomials
Journal of Computational and Applied Mathematics
Condition Numbers of Random Triangular Matrices
SIAM Journal on Matrix Analysis and Applications
A Parallel Algorithm to Evaluate Chebyshev Series on a Message Passing Environment
SIAM Journal on Scientific Computing
The Complexity of Parallel Evaluation of Linear Recurrences
Journal of the ACM (JACM)
Parallel Tridiagonal Equation Solvers
ACM Transactions on Mathematical Software (TOMS)
Parallel Algorithms to Evaluate Orthogonal Polynomial Series
SIAM Journal on Scientific Computing
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Solving Linear Systems on Vector and Shared Memory Computers
Solving Linear Systems on Vector and Shared Memory Computers
Journal of Computational and Applied Mathematics
Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces I: algorithms
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces I: algorithms
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Evaluating linear recursive filters using novel data formats for dense matrices
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
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We present some remarks on the numerical evaluation of recurrence relations. Rounding error bounds are presented of the numerical scheme and some numerical examples are given, in particular, we analyse conversion recurrences from different families of orthogonal polynomials, the limit case of Jacobi-Sobolev polynomials, random recurrences and perturbed Gegenbauer polynomials. In all these examples the theoretical bounds give sharp relative rounding error estimations. The parallel evaluation of recurrences are also considered and numerical tests on a Cray T3D are presented.