On basic concepts in parallel numerical mathematics

  • U. Schendel
Nonnumerical Parallel Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 111)


Parallel Algorithm Recurrent System Parallel Evaluation Arithmetic Expression Recurrence Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    BAUDET, G.M. Asynchronous Iterative Methods for Multiprocessors Dep. of Comp. Sci., Carnegie-Mellon Univ., Pittsburgh, Pa., 1976Google Scholar
  2. [2]
    BORODIN, A./MUNRO, I. The Computational Complexity of Algebraic and Numeric Problems American Elsevier Publ. Comp. (1975)Google Scholar
  3. [3]
    BRENT, R.P. The Parallel Evaluation of Arithmetic Expressions in Logarithmic Time in: Traub, J.F. (ed), Complexity of Sequential and Parallel Numerical Algorithms, Academic Press, 1973, p. 83–102Google Scholar
  4. [4]
    BRENT, R.P. The Parallel Evaluation of General Arithmetic Expressions J. ACM 21, 2(1974) 201–206zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    BRENT, R.P./KUCK, D./MARUYAMA, K. The Parallel Evaluation of Arithmetic Expressions Without Division IEEE Trans. Comp. C-22, (1973) 533–534MathSciNetGoogle Scholar
  6. [6]
    EVANS, D.J./HATZOPOULOS, M. A Parallel Linear Systems Solver Intern. J. Computer Math. 7, 3(1979) 227–238zbMATHMathSciNetGoogle Scholar
  7. [7]
    FEILMEIER, M./GOMM, W./RÖNSCH, W./TÖPFER, K. Parallele Numerik DFG-Bericht, to appearGoogle Scholar
  8. [8]
    FEILMEIER, M./SEGERER, G. Numerical Stability in Parallel Evaluation of Arithmetic Expressions in: Feilmeier, M. (ed), Parallel Computers — Parallel Mathematics, North-Holland Publ. Co., Amsterdam, 1977, p. 107–112Google Scholar
  9. [9]
    FLYNN, M. Some Computer Organizations and their Effectiveness IEEE Trans. Comp. C-21, 9(1972) 948–960MathSciNetCrossRefGoogle Scholar
  10. [10]
    Händler, W. Innovative Computer Architecture: How to enlarge Parallelism and not ComplexityGoogle Scholar
  11. [11]
    HYAFIL, L./KUNG, H.T. The Complexity of Parallel Evaluation of Linear Recurrences J. ACM 24, 3(1977) 513–521zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    KOBER, R./KUZNIA, C. SMS 201 — A Powerful Parallel Processor with 128 Microcomputers Euromicro J. 5, 1(1979) 48–52CrossRefGoogle Scholar
  13. [13]
    KOGGE, P.M. Parallel Algorithms for the Efficient Solution of Recurrence Problems; The Numerical Stability of Parallel Algorithms for Solving Recurrence Problems; Minimal Parallelism in the Solution of Recurrence Problems Stanford Univ., Ca., Stanford Electronics Labs., Sept. 1972, PB-212893, PB-212894, PB-212828Google Scholar
  14. [14]
    KOGGE, P.M. Parallel Solution or Recurrence Problems IBM J. Res. Develop. 18, 2(1974) 138–148zbMATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    LAMBIOTTE, J.J./VOIGT, R.G. The Solution of Tridiagonal Linear Systems on the CDC STAR-100 Computer ACM Trans. Math. Softw. 1, (1975) 308–329zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    MADSEN, N.K./RODRIGUE, G.H. A Comparison of Direct Methods for Tridiagonal Systems on the CDC STAR-100 Lawrence Livermore Lab. Livermore CA., 1975Google Scholar
  17. [17]
    MADSEN, N.K./RODRIGUE, G.H. Odd-Even Reduction of Pentadiagonal Matrices in: Feilmeier, M. (ed.), Parallel Computers-Parallel Mathematics, North-Holland Publ. Co., Amsterdam, 1977, p. 103–106Google Scholar
  18. [18]
    MIRANKER, W.L. Parallel Search Methods for Solving Equations in: Feilmeier, M. (ed), Parallel Computers-Parallel Mathematics, North-Holland Publ. Co., Amsterdam 1977 p. 9–15 and Math. Comp. Simul. 20, 2(1978) 93–101Google Scholar
  19. [19]
    MOISKE, B./SCHENDEL, U. Code-Optimierung für arithmetische Ausdrücke 1981 (to appear)Google Scholar
  20. [20]
    NAGEL, K. Lösung linearer Gleichungssysteme nach dem Gauß-Seidelverfahren auf dem Parallelrechner SMS 201 Notiz, 1978Google Scholar
  21. [21]
    SAMEH, A.H./BRENT, R.P. Solving Triangular Systems on a Parallel Computer SIAM J. Num. Anal. 14, 6(1977) 1101–1113zbMATHCrossRefMathSciNetGoogle Scholar
  22. [22]
    SAMEH, A.H./KUCK, D.J. Parallel Direct Linear System Solvers — A Survey in: Parallel Computers — Parallel Mathematics Ed. M. Feilmeier, München 1977Google Scholar
  23. [23]
    SCHENDEL, U. Rekurrente Relationen in: Parallele Datenverarbeitung und parallele Algorithmen Brennpunkt Kybernetik, TU-Berlin, Band 68, (1979)Google Scholar
  24. [24]
    SCHENDEL, U. Parallel Algorithms Report of the Computer Science Department, University of Natal, Durban, South Africa (1977)Google Scholar
  25. [25]
    SCHENDEL, U./BRANDENBURGER, J. Algorithmen zur Lösung Rekurrenter Relationen Preprint Nr. 101/79, Freie Universität Berlin (1979)Google Scholar
  26. [26]
    SWARZTRAUBER, P. N. A Parallel Algorithm for Solving General Tridiagonal Equations Math. Comp. 33, 145(1979) 185–199zbMATHCrossRefMathSciNetGoogle Scholar
  27. [27]
    TRAUB, J.F. Iterative Solution of Tridiagonal Systems on Parallel or Vector Computers in: Traub, J.F. (ed), Complexity of Sequential and Parallel Numerical Algorithms, Academic Press, New York, 1973, p. 49–82Google Scholar
  28. [28]
    WALLACH, Y./KONRAD, V. On Block-Parallel Methods for Solving Linear Equations IEEE Trans. Comp. C-29, 5(1980) 354–359Google Scholar
  29. [29]
    WINOGRAD, S. On the Parallel Evaluation of Certain Arithmetic Expressions J. ACM 22, 4(1975) 477–492zbMATHCrossRefMathSciNetGoogle Scholar
  30. [30]
    WORLAND, P.B. Parallel Methods for the Numerical Solution of Ordinary Differential Equations IEEE Trans. Comp. C-25, 10(1976) 1045–1048MathSciNetGoogle Scholar
  31. [31]
    AHO, A.V./JOHNSON, S.C. Optimal Code Generation for Expression Trees J. ACM, 76Google Scholar
  32. [32]
    PRAUSE, D. Parallelisierung von Optimierungsproblemen TU Braunschweig, 1980Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • U. Schendel
    • 1
  1. 1.Institut für Mathematik IIIFreie Universität BerlinGermany

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