The granularity of parallel homotopy algorithms for polynomial systems of equations

References

• Allgower , E. and Georg , K. 1980 . Simplicial and continuation methods for approximating fixed points . SIAM Rev. , 22 : 28 – 85 .
   Web of Science ®Google Scholar
• Billups , S. C. 1985 . Linear least squares solutions by Householder transformations . Numer. Math. , 7
   Google Scholar
• Businger , P. and Golub , G. H. 1965 . Linear least squares solutions by Householder transformations . Numer. Math. , 7 : 269 – 276 .
   Google Scholar
• Chen , A. C. and Wu , C. L. 1984 . Proc. Internat. Conf. on Parallel Processing . Optimum Solution to Dense Linear Systems of Equations . August 21-24 1984 . pp. 417 – 425 .
   Google Scholar
• Chen , M. Y. and Murata , T. . Proc. Internat. Conf. on Parallel Processing . Fast Algorithm for Concurrent LU Decomposition and Matrix Inversion . Los Alamitos. pp. 79 – 86 . CA : Computer Society Press .
   Google Scholar
• Chow , S. N. , Mallet-Paret , J. and Yorke , J. A. 1978 . Finding zeros of maps: Homotopy methods that are constructive with probability one . Math. Comput. , 32 : 887 – 899 .
   Web of Science ®Google Scholar
• Cloéte , E. and Joubert , G. R. 1982 . Proc. 8th South African Symp. on Numerical Mathematics . Direct Methods for Solving Systems of Linear Equations on a Parallel Processor . July 19-21 1982 , Durban, South Africa.
   Google Scholar
• Chow , S. N. , Mallet-Paret , J. and Yorke , J. A. 1988 . Finding zeros of maps: Homotopy methods that are constructive with probability one . Math. Comput. , 781 : 887 – 899 .
   Google Scholar
• Ellis , G. H. and Watson , L. T. 1984 . A parallel algorithm for simple roots of polynomials . Comput. Math. Appl. , 10 July : 107 – 121 .
   Google Scholar
• Gajski , D. , Sameh , A. H. and Wisniewski , J. A. 1982 . Proc. Internat. Conf. Parallel Processing . Iterative Algorithms for Tridiagonal Matrices on a WSI-multiprocessor . August 24-27 1982 , Bellaire, MI. pp. 82 – 89 .
   Google Scholar
• Gentzsch , W. and Schafer , G. 1984 . “ Parallel Computing 83 ” . In Solution of Large Linear Systems on Vector Computers , 159 – 166 . Amsterdam : North Holland .
   Google Scholar
• Heller , D. 1978 . A survey of parallel algorithms in numerical linear algebra . SIAM Rev. , 20 : 740 – 777 .
   Web of Science ®Google Scholar
• Heller , D. 1978 . A survey of parallel algorithms in numerical linear algebra . SIAM Rev. , 20 : 740 – 777 .
   Web of Science ®Google Scholar
• Kaneda , Y. and Kohata , M. 1982 . 10th IMACS World Congress . Highly Parallel Computing of Linear Equations on the Matrix-Broadcast-Memory Connected Array Processor System , 1-5 : 320 – 322 .
   Google Scholar
• Kowalik , J. S. 1982 . Proc. IEEE 1982 Internat. Conf. on Cybernetics and Society . Parallel Computation of Linear Recurrences and Tridiagonal Equations . 1982 . pp. 580 – 584 .
   Google Scholar
• Kowalik , J. S. and Kumar , S. P. 1982 . Proc. Internat. Conf. Parallel Processing . An Efficient Parallel Block Conjugate Gradient Method for Linear Equations . August 24-27 1982 , Bellaire, MI. pp. 47 – 52 .
   Google Scholar
• Kubicek , M. 1976 . Dependence of solutions of nonlinear systems on a parameter . ACM Trans. Math. Software , 2 August : 98 – 107 .
   Google Scholar
• Lakshmivarahan S. Dhall S. K. Parallel Algorithms for Solving Certain Classes of Linear Recurrences Foundations of Software Technology and Theoretical Computer Science Lecture Notes in Computer Science 206 Springer-Verlag Berlin 1985 457 477
   Google Scholar
• Morgan , A. P. 1986 . A transformation to avoid solutions at infinity for polynomial systems . Appl. Math. Comput. , 18 August : 77 – 86 .
   Google Scholar
• Morgan , A. P. 1986 . A homotopy for solving polynomial systems . Appl. Math. Comput. , 18 August : 87 – 92 .
   Web of Science ®Google Scholar
• Morgan , A. P. 1987 . Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Morgan , A. P. and Watson , L. T. A globally convergent parallel algorithm for zeros of polynomial systems . J. Parallel Distributed Comput. , to appear
   Google Scholar
• Parkinson , D. 1984 . “ Parallel Computing 83 ” . In The Solution of N Linear Equations Using P Processors , 81 – 87 . Amsterdam : North Holland .
   Google Scholar
• Pelz , W. and Watson , L. T. Message length effects for solving polynomial systems on a hypercube . Parallel Comput. , to appear
   Google Scholar
• Reed , D. A. and Patrick , M. L . 1984 . Proc. 1984 Internat. Conf. on Parallel Processing . A Model of Asynchronous Iterative Algorithms for Solving Large Sparse Linear Systems . August 21-24 1984 . pp. 402 – 410 .
   Google Scholar
• Rheinboldt , W. C. and Burkardt , J. V. 1983 . Algorithm 596: A program for a locally parameterized continuation process . ACM Trans. Math. Software , 9 August : 236 – 241 .
   Web of Science ®Google Scholar
• Rice , T. A. and Siegel , L. J. 1982 . Proc. Internat. Conf. Parallel Processing . A Parallel Algorithm for Finding the Roots of a Polynomial . August 24-27 1982 , Bellaire, MI. pp. 57 – 61 .
   Google Scholar
• Schwandt , H. 1985 . Newton-like interval methods for large nonlinear systems of equations on vector computers . Computer Phys. Comm. , 37 August : 223 – 232 .
   Google Scholar
• Seitz , C. L. 1985 . The cosmic cube . Commun. ACM , 28 August : 22 – 23 .
   Web of Science ®Google Scholar
• Shampine , L. F. and Gordon , M. K. 1975 . Computer Solution of Ordinary Differential Equations: The Initial Value Problem , San Francisco : W. H. Freeman .
   Google Scholar
• Sips , H. J. . Proc. 1st Internat. Conf. on Supercomputing Systems . A Parallel Processor for Nonlinear Recurrence Systems . pp. 660 – 671 . Los Alamitos, CA : IEEE Computer Society Press .
   Google Scholar
• Watson , L. T. and Fenner , D. 1980 . Chow-Yorke algorithm for fixed points or zeros of C 2 maps . ACM Trans. Math. Software , 6 : 252 – 260 .
   Google Scholar
• Watson , L. T. 1979 . A globally convergent algorithm for computing fixed points of C 2 maps . Appl. Math. Comput. , 5 : 297 – 311 .
   Google Scholar
• Watson L. T. Billups S. C. Morgan A. P. Hompack: A Suite of Codes for Globally Convergent Homotopy Algorithms Tech. Rep. 85-34 Dept. of Industrial and Operations Eng., University of Michigan 1987 281 310
   Google Scholar
• Watson L. T. Numerical Linear Algebra Aspects of Globally Convergent Homotopy Methods Tech. Report TR-85-14, Dept, of Computer Sci., VPI & SU, Blacksburg, VA, 1985 and SIAM Rev. 28 1986 529 545
   Google Scholar
• White , R. 1986 . Parallel algorithms for nonlinear problems . SIAM J. Algebraic Discrete Methods , 7 : 137 – 149 .
   Google Scholar
• White , R. 1986 . A nonlinear parallel algorithm with application to the Stefan problem . SIAM J. Numer. Anal. , 23 : 639 – 652 .
   Web of Science ®Google Scholar