Parallel algorithms to evaluate orthogonal polynomial series

SIAM Journal on Scientific Computing

Volumn 21, Issue 6, 2000, Pages 2225-2239

  Barrio, Roberto ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CHEBYSHEV POLYNOMIALS; CLENSHAW SEQUENTIAL ALGORITHMS; FORSYTHE SEQUENTIAL ALGORITHMS; ORTHOGONAL POLYNOMIALS; POLYNOMIAL EVALUATION;

ASYMPTOTIC STABILITY; COMPUTATIONAL COMPLEXITY; LINEAR SYSTEMS; MATRIX ALGEBRA; PARALLEL ALGORITHMS; PARALLEL PROCESSING SYSTEMS;

POLYNOMIALS;

EID: 0034506023     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827598340494     Document Type: Article

References (30)

1. M. ABRAMOWITZ AND I. A. STEGUN, Handbook of Mathematical Functions, Dover Publications, Inc., New York, 1965.
2. R. ASKEY, Orthogonal Polynomials and Special Functions, SIAM, Philadelphia, PA, 1975.
3. R. BARRIO AND J. C. BERGES, Perturbation simulations of rounding errors in the evaluation of Chebyshev series, J. Univ. Comp. Sci., 4 (1998), pp. 561-573.
4. R. BARRIO AND F. J. SABADELL, A parallel algorithm to evaluate Chebyshev series on a message-passing environment, SIAM J. Sci. Comput., 20 (1998), pp. 964-969.
5. R. BARRIO AND F. J. SABADELL, Parallel evaluation of Chebyshev and trigonometric series, Comput. Math. Appl., 38 (1999), pp. 99-106.
6. S. BOOTH, D. HENTY, P. MACCALLUM, N. MACDONALD, A. SIMPSON, AND S. PATON, Performance Optimisation on the Cray T3D, EPCC, University of Edinburgh, UK, 1997.
7. S. C. CHEN, D. J. KUCK, AND A. H. SAMEH, Practical parallel band triangular system solvers, ACM Trans. Math. Software, 4 (1978), pp. 270-277.
8. C. W. CLENSHAW, A note on the summation of Chebyshev series, Math. Tab. Wash., 9 (1955), pp. 118-120.
9. J. J. DONGARRA, I. S. DUFF, D. C. SORENSEN, AND H. A. VAN DER VORST, Solving Linear Systems on Vector and Shared Memory Computers, SIAM, Philadelphia, PA, 1991.
10. J. J. DONGARRA AND S. L. JOHNSSON, Solving banded systems on a parallel processor, Parallel Comput., 5 (1987), pp. 219-246.
11. W. S. DORN, Generalisations of Horner's rule for polynomial evaluation, IBM J. Res. Develop., 6 (1962), pp. 239-245.
12. G. E. FORSYTHE, Generation and use of orthogonal polynomials for data fitting with a digital computer, J. SIAM, 5 (1957), pp. 74-88.
13. N. J. HIGHAM, The accuracy of floating point summation, SIAM J. Sci. Comput., 14 (1993), pp. 783-799.
14. N. J. HIGHAM, Stability of parallel triangular solvers, SIAM J. Sci. Comput., 16 (1995), pp. 400-413.
15. S. L. JOHNSSON, Solving tridiagonal systems on ensemble of architectures, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 354-392.
16. S. L. JOHNSSON, Solving narrow banded systems on ensemble of architectures, ACM Trans. Math. Software, 11 (1985), pp. 271-288.
17. A. KIPER, Parallel polynomial evaluation by decoupling algorithm, Parallel Algorithms Appli., 9 (1996), pp. 145-152.
18. A. KIPER, Modified Dorn's algorithm with improved speed-up, in Applied Parallel Computing: Industrial Computation and Optimization, Lecture Notes Comput. Sci. 1184, J. Wasniewski, ed., Springer-Verlag, New York, 1997, pp. 432-442.
19. L. LI, J. HU, AND T. NAKAMURA, A simple parallel algorithm for polynomial evaluation, SIAM J. Sci. Comput., 17 (1996), pp. 260-262.
20. W. MAGNUS, F. OBERHETTINGER, AND R. P. SONI, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, New York, 1966.
21. K. MARUYAMA, On the parallel evaluation of polynomials, IEEE Trans. Comput., C-22 (1973), pp. 2-5.
22. U. MEIER, A parallel partition method for solving banded systems of linear equations, Parallel Comput. 2 (1985), pp. 33-43.
23. J. I. MUNRO AND M. PATERSON, Optimal algorithms for parallel polynomial evaluation, J. Comput. System Sci., 7 (1973), pp. 189-198.
24. R. E. OVERILL AND S. WILSON, Performance of parallel algorithms for the evaluation of power series, Parallel Computing, 20 (1994), pp. 1205-1213.
25. F. J. SMITH, An algorithm for summing orthogonal polynomial series and their derivatives with applications to curve-fitting and interpolation, Math. Comput., 19 (1965), pp. 33-36.
26. H. S. STONE, Parallel tridiagonal equations solvers, ACM Trans. Math. Software, 1 (1975), pp. 289-307.
27. P. N. SWARZTRAUBER, A parallel algorithm for solving general tridiagonal equations, Math. Comput., 33 (1979), pp. 185-199.
28. H. H. WANG, A parallel method for tridiagonal equations, ACM Trans. Math. Software, 7 (1981), pp. 170-183.
29. P. Y. YALAMOV, Stability of parallel bidiagonal solvers, in Parallel Scientific Computing PARA'94, Lecture Notes Comput. Sci. 879, Springer-Verlag, New York, 1994, pp. 520-533.
30. P. Y. YALAMOV, Stability of a partitioning algorithm for bidiagonal systems, Parallel Comput., 23 (1997), pp. 333-348.