Recent advances in solvers for nonlinear alegebraic equations
Abstract
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.
References
[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. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen. LAPACK 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.
[2] E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen. LAPACK 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.
Published
2023-03-29
Issue
pp. 493-505
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Dent, D., Paprzycki, M., & Kucaba-Piętal, A. (2023). Recent advances in solvers for nonlinear alegebraic equations. Computer Assisted Methods in Engineering and Science, 7(4), 493-505. https://cames3.ippt.pan.pl/index.php/cames/article/view/1207
