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Recent advances in solvers for nonlinear algebraic equations

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Konferencja
Polish Conference on Computer methods in mechanics ; (14 ; 26-28.05.1999 ; Rzeszów, Poland
Języki publikacji
EN
Abstrakty
EN
In this paper the performance of four solvers for systems of nonlinear algebraic equations applied to a number of test problems with up to 250 equations is discussed. These problems have been collected from research papers and from the Internet and are often recognized as ``standard'' tests. Solver quality is assessed by studying their convergence and sensitivity to simple starting vectors. Experimental data is also used to categorize the test problems themselves. Future research directions are summarized.
Słowa kluczowe
Rocznik
Strony
493--505
Opis fizyczny
Bibliogr. 24 poz., tab.
Twórcy
autor
  • School of Mathematical Sciences, University of Southern Mississippi, Hattiesburg, MS 39406-5106, USA
autor
  • School of Mathematical Sciences, University of Southern Mississippi, Hattiesburg, MS 39406-5106, USA
  • Department of Fluid Mechanics and Aerodynamics, Technical University of Rzeszów
Bibliografia
  • [1] E. Allgowerr, K. George. Numerical Continuation Methods: An Introduction. Springer-Verlag, Berlin, 365, 1990.
  • [2] E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammaxling, A. McKenney, S. Ostrouchov, D. Sorensen. LAPA CK Users' Guide. SIAM, Philadelphia, 1994.
  • [3] A. Bouaricha, R. Schnabel. Algorithm 768: TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least-squares problems using tensor methods. ACM Trans. Math. Software, 23(2): 174-195, 1997.
  • [4] R. L. Burden, J. D. Faries. Numerical Analysis, 575-576. PWS-Kent Publishing Company, Boston, 1993.
  • [5] D. Dent, M. Paprzycki, A. Kucaba-Piętal. Performance of solvers for systems of nonlinear algebraic equations. Proceedings of 15th Annual Conf. on Applied Math, Edmond, OK, 67-77, 1999.
  • [6] D. Dent, M. Paprzycki, A. Kucaba-Piętal. Studying the numerical properties of solvers for systems of nonlinear equations. Proceedings of the Ninth International Colloquium on Differential Equations VSP, Utrecht, The Netherlands, 113-118, 1999.
  • [7] D. Dent, M. Paprzycki, A. Kucaba-Piętal. Testing convergence of nonlinear system solvers. FSCC, 1, http : //pax . st . usm. edu/cmi/f s cc98_html/processed/, 1999.
  • [8] G. H. Hostetter, M. S. Santina, P. D'Capio-Montalvo. Analytical, Numerical and Computational Methods for Science and Engineering. Prentice Hall, Englewood Cliffs, 1991.
  • [9] A. Kucaba-Piętal, L. Laudanski. Modeling Stationary Gaussian Loads. Scientific Papers of Silesian Technical University, Mechanics, textbf121, 173-181, 1995.
  • [10] L. Laudanski. Designing random vibration tests. Int. J. Non-Linear Mechanics, 31(5): 563-572, 1996.
  • [11] J. J. More. A collection of nonlinear model problems. Amer. Math. Soc., 26, 723-762, 1990.
  • [12] J. J. More, B. S. Garbow, K. E. Hillstrom. Algorithm 566. ACM Trans, Math. Software, 20(3): 282-285, 1994.
  • [13] J. J. More, D.C. Sorensen, K. E. Hillstrom, B. S. Garbow. The MINPACK Project, in Sources and Development of Mathematical Software. Prentice-Hall, 1984.
  • [14] NEOS Guide. http: //www-fp.mcs .ani .gov/otc/Guide/, 1996.
  • [15] Netlib Repository. http: //www.netlib.org/liblist .html, 1999.
  • [16] M. J. D. Powell. A Hybrid Method for Nonlinear Algebraic Equations (in Polish). Gordon and Breach, Rabinowitz, 1979.
  • [17] W. C. Rheinboldt. Methods for Solving System of Nonlinear Equations. SIAM, Philadelphia, 1998.
  • [18] W. C. Rheinboldt, J. Burkardt. Algorithm 596: A program for a locally parametrized continuation process. ACM Trans. Math. Software, 9: 236-241, 1983.
  • [19] R. B. Schnabel, P. Frank. Tensor methods for nonlinear equations. SIAM J. Numer. Anal., 21: 814-843, 1984.
  • [20] J. Stoer, R. Bulirsh. Introduction to Numerical Analysis. Springer, New York, 521, 1993.
  • [21] L. T. Watson. personal communication.
  • [22] L. T. Watson, M. Sosonkina, R. C. Melville, A. P. Morgan, H. F. Walker. Algorithm 777: HOMPACK 90: Suite of Fortran 90 codes for globally convergent homotopy algorithms. ACM Trans. Math. Software, 23(4): 514-549, 1997.
  • [23] L. T. Watson, S. C. Billups, A. P. Morgan. Algorithm 652:HOMPACK: A suite of codes for globally convergent homotopy algorithms. ACM Trans. Math. Software, 13: 281-310, 1987.
  • [24] U. N. Weimann. A family of Newton codes for systems of highly nonlinear equations. ZIB Technical Report TR-91-10. ZIB, Berlin, Germany, 1991.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0005-0018
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