Tensor methods for large sparse systems of nonlinear equations

Mathematical Programming, Series B

Volumn 82, Issue 3, 1998, Pages 377-400

  Bouaricha, Ali ^a   Schnabel, Robert B ^b  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b University of Colorado at Boulder   (United States)

Author keywords

Nonlinear equations; Rank deficient matrices; Sparse problems; Tensor methods

Indexed keywords

EID: 0042355443     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01580076     Document Type: Article

References (22)

1. Å. Björck, I.S. Duff, A direct method for the solution of sparse linear least squares problems, Linear Algebra Appl. 34 (1980) 43-67.
2. B.M. Averick, R.G. Carter, J.J. Moré, G.L. Xue, The MINPACK-2 test problem collection, Preprint MCS-P153-0692, Mathematics and Computer Science Division, Argonne National Laboratory, 1992.
3. A. Bouaricha, Solving Large Sparse Systems of Nonlinear Equations and Nonlinear Least Squares Problems Using Tensor Methods on Sequential and Parallel Computers, PhD Thesis, Computer Science Department, University of Colorado at Boulder, 1992.
4. A. Bouaricha, R.B. 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 (1997) 174-195.
5. A.E. Bryson, A.E. Ho, Applied Optimal Control, Chap. 2, Wiley, New York, 1975.
6. T.F. Coleman, B.S. Garbow, J.J. Moré, Fortran subroutines for estimating sparse Jacobian matrices, ACM Trans. Math. Software 10 (1984) 346-347.
7. T.F. Coleman, B.S. Garbow, J.J. Moré, Software for estimating sparse Jacobian matrices, ACM Trans. Math. Software 10 (1984) 329-345.
8. T.F. Coleman, J.J. Moré, Estimation of sparse Jacobian matrices and graph coloring problems, SIAM J. Numer. Anal. 20 (1983) 187-207.
9. D.W. Decker, C.T. Kelly, Newton's method at singular points I, SIAM J. Numer. Anal. 17 (1980) 66-70.
10. D.W. Decker, C.T. Kelly, Newton's method at singular points II, SIAM J. Numer. Anal. 17 (1980) 465-471.
11. I.S. Duff, MA28: A set of Fortran subroutines for sparse unsymmetric linear equations, Technical Report R-8730, AERE Harwell Laboratory, 1977.
12. D. Feng, P. Frank, R.B. Schnabel, Local convergence analysis of tensor methods for nonlinear equations, Math. Programming 62 (1993) 427-459.
13. P.D. Frank, W.P. Huffman, Parallel solution of large and sparse nonlinear systems, Technical Report ECA-TR-128, Boeing Computer Services, 1989.
14. Andreas Griewank, On automatic differentiation, in: Mathematical Programming: Recent Developments and Applications, Kluwer Academic Publishers, Dordrecht, 1989, pp. 83-108.
15. Andreas Griewank, George F. Corliss (Eds.), Automatic Differentiation of Algorithms: Theory, Implementation, and Application, Society for Industrial and Applied Mathematics, 1991.
16. J.J. Moré, A collection of nonlinear model problems, in: E.L. Allgower, K. Georg (Eds.), Computational Solutions of Nonlinear Systems of Equations, Lecture Notes in Applied Mathematics, vol. 26, American Mathematical Society, Providence, RI, 1990, pp. 723-762.
17. J.J. Moré, B.S. Garbow, K.E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software 7 (1981) 17-41.
18. J.J. Moré, D.C. Sorensen, Computing a trust region step, SIAM J. Sci. Statist. Comput. 4 (1983) 553-572.
19. N. Munksgaard, NS02: A Fortran subroutine for solving sparse sets of nonlinear equations by Powell's Dog-leg algorithm, Technical Report R-11047, AERE Harwell Laboratory, 1938.
20. G. Peters, J.H. Wilkinson, The least squares problem and pseudo-inverses, Comput. J. 13 (1970) 309-316.
21. R.B. Schnabel, P.D. Frank, Tensor methods for nonlinear equations, SIAM J. Numer. Anal. 21 (1984) 815-843.
22. A. Bouaricha, R.B. Schnabel, Tensor methods for large, sparse nonlinear least squares problems, SIAM J. Scientific Comput. (to appear).