论文信息 - Three new algorithms based on the sequential secant method

Three new algorithms based on the sequential secant method

We introduce three new implementations of the sequential secant method for solving nonlinear simultaneous equations. Following the ideas of Gragg and Stewart, we store orthogonal factorizations of some of the matrices involved. Degeneracy in the increments of the independent variable is corrected according to simple and theoretically justified procedures. Some numerical experiences are also given.

José Mario Martínez | J. Martínez

[1] José Mario Martínez,et al. On the order of convergence of Broyden-Gay-Schnabel's method , 1978 .

[2] Janina Jankowska,et al. Theory of Multivariate Secant Methods , 1979 .

[3] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[4] R. Schnabel,et al. Solving Systems of Non-Linear Equations by Broyden&Apos;S Method with Projected Updates , 1977 .

[5] J. J. Moré,et al. On the Global Convergence of Broyden''s Method , 1974 .

[6] Philip Wolfe,et al. The Secant method for simultaneous nonlinear equations , 1959, CACM.

[7] G. Stewart,et al. A Stable Variant of the Secant Method for Solving Nonlinear Equations , 1976 .

[8] H. Woźniakowski,et al. Numerical stability for solving nonlinear equations , 1976 .

[9] John Grover Barnes,et al. An Algorithm for Solving Non-Linear Equations Based on the Secant Method , 1965, Comput. J..

[10] G. Stewart,et al. Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization , 1976 .

[11] John Grover Barnes,et al. A KDF9 ALGOL list-processing scheme , 1965, Comput. J..