Continuation methods for the solution of nonlinear equations

44. J. P. Abbott and R. P. Brent, A note on continuation methods for the solution of nonlinear equations, J. Australian Mathematical Society (Series B) 20 (1978), 157-164. MR 58\#13672.

Paper: pdf (658K).

Abstract

We present a variable-order continuation method for the solution of nonlinear equations when only a poor estimate of a solution is known. The method changes continuously from one which improves the global convergence characteristics to one which attains rapid convergence to a solution and proves to be more efficient than methods previously presented in [30].

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