Studying the Performance Nonlinear Systems Solvers Applied to the Random Vibration Test

  • Deborah Dent
  • Marcin Paprzycki
  • Anna Kucaba-Pię
  • Ludomir Laudánski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2179)


In this paper we compare the performance of four solvers for systems of nonlinear algebraic equations applied to the random vibration test, which requires a solution of a system of 512 or more equations. Experimental results obtained for two test cases are presented and discussed.


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  1. 1.
    A. Bouaricha and 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.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. R. Conn, M. I. M. Gould, and P. L. Toint. LANCELOT: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A), Springer-Verlag, New York, 1992.zbMATHGoogle Scholar
  3. 3.
    D. Dent, M. Paprzycki, and A. Kucaba-Pietal. Testing convergence of nonlinear system solvers, in Proceedings of the First Southern Symposium on Computing, Hattiesburg, MS, CD, file, 1999.Google Scholar
  4. 4.
    D. Dent, M. Paprzycki, and A. Kucaba-Pietal. Solvers for systems of nonlinear algebraic equations-their sensitivity to starting vectors, in Numerical Analysis and Its Applications, Lecture Notes in Computer Science, 1988, Spinger Verlag, 230–238, 2001.Google Scholar
  5. 5.
    K. W. Fong, T. H. Jefferson, and T. Suyehiro. Guide to the SLATEC common mathematical library, Technical Report Energy Science and Technology Software Center, Oak Ridge, TN, 1993.Google Scholar
  6. 6.
    R. B. Kearfott and M. Novoa III. Algorithm 681 INTLIB, a portable interval Newton/bisection package, ACM Transactions on Mathematical Software, 16(2), 152–157, 1990.zbMATHCrossRefGoogle Scholar
  7. 7.
    A. Kucaba-Pietal and L. Laudanski. Modeling stationary Gaussian loads, Scientific Papers of Silesian Technical University, Mechanics, 121, 173–181, 1995.Google Scholar
  8. 8.
    L. Laudanski. Designing random vibration tests, Int. J. Non-Linear Mechanics, 31 (5), 563–572, 1996.CrossRefGoogle Scholar
  9. 9.
    B. A. Murtagh and M. A. Saunders. MINOS 5.4 USER’S GUIDE, Technical Report SOL83-20R, Department of Operations Research, Standford University, Standford, California, USA, 1993, (Revised 1995).Google Scholar
  10. 10.
    M. J. D. Powell. A hybrid method for nonlinear algebraic equations, Gordon and Breach, Rabinowitz, 1979.Google Scholar
  11. 11.
    W. C. Rheinboldt and J. Burkardt. Algorithm 596: A program for a locally parameterized continuation process, ACM Trans. Math. Software, 9, 236–241, 1983.CrossRefMathSciNetGoogle Scholar
  12. 12.
    L. T. Watson, M. Sosonkina, R. C. M elville, A. P. Morgan, and 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.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    M. N. Vrahatis. Algorithm 666: CHABIS: A mathematical software package systems of nonlinear equations, ACM Transactions on Mathematical Software, 4(4), 312–329, 1988.CrossRefMathSciNetGoogle Scholar
  14. 14.
  15. 15.
    Netlib Repository,, 1999.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Deborah Dent
    • 1
  • Marcin Paprzycki
    • 1
  • Anna Kucaba-Pię
    • 2
  • Ludomir Laudánski
    • 2
  1. 1.School of Mathematical SciencesUniversity of Southern MississippiHattiesburgUSA
  2. 2.Department of Fluid Mechanics and AerodynamicsRzeszow University of TechnologyRzeszxówPoland

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