Parallel Newton Two-Stage Multisplitting Iterative Methods for Nonlinear Systems
Tóm tắt
Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorithms are based on both the multisplitting technique and the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms studied, computational results about these methods on a distributed memory multiprocessor are discussed.
Tài liệu tham khảo
J. Arnal, V. Migallón, and J. Penadés, Non-stationary parallel multisplitting algorithms for almost linear systems, Numer. Linear Algebra Appl., 6 (1999), pp. 79-92.
J. Arnal, V. Migallón, and J. Penadés, Synchronous and asynchronous parallel algorithms with overlap for almost linear systems, in Lectures Notes in Comput. Sci. 1573, 1999, pp. 142-155.
J. Arnal, V. Migallón, and J. Penadés, Non-stationary parallel Newton iterative methods for nonlinear problems, in Lectures Notes in Comput. Sci. 1981, 2001, pp. 380-394.
B. M. Averick, R. G. Carter, J. J. More, and G. Xue, The MINPACK-2 Test Problem Collection, Tech. Report, MCS-P153-0692, Mathematics and Computer Science Division, Argonne National Laboratory, 1992.
J. Bahi, J. C. Miellou, and K. Rhofir, Asynchronous multisplitting methods for nonlinear fixed point problems, Numer. Algorithms, 15(3) (1997), pp. 315-345.
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 3rd ed., 1979. Reprinted by SIAM, Philadelphia, 1994.
R. Bru, L. Elsner, and M. Neumann, Models of parallel chaotic iteration methods, Linear Algebra Appl., 103 (1988), pp. 175-192.
R. Bru, V. Migallón, J. Penadés, and D. B. Szyld, Parallel, synchronous and asynchronous two-stage multisplitting methods, Electron. Trans. Numer. Anal., 3 (1995), pp. 24-38.
R. S. Dembo, S. C. Eisenstat, and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal., 19(2) (1982), pp. 400-408.
A. Frommer, Parallel nonlinear multisplitting methods, Numer. Math., 56 (1989), pp. 269-282.
A. Frommer and G. Mayer, Convergence of relaxed parallel multisplitting methods, Linear Algebra Appl., 119 (1989), pp. 141-152.
A. Frommer and D. B. Szyld, H-splittings and two-stage iterative methods, Numer. Math., 63 (1992), pp. 345-356.
J. Mas, V. Migallón, J. Penadés, and D. B. Szyld, Non-stationary parallel relaxed multisplitting methods, Linear Algebra Appl., 241/243 (1996), pp. 733-748.
D. P. O'Leary and R. E. White, Multi-splittings of matrices and parallel solution of linear systems, SIAM J. Alg. Discrete Meth., 6 (1985), pp. 630-640.
J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, San Diego, 1970.
A. Sherman, On Newton-iterative methods for the solution of systems of nonlinear equations, SIAM J. Numer. Anal., 15 (1978), pp. 755-771.
R. E. White, Parallel algorithms for nonlinear problems, SIAM J. Alg. Discrete Meth., 7 (1986), pp. 137-149.