Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4636186 | Applied Mathematics and Computation | 2006 | 5 Pages |
Abstract
We provide new sufficient conditions for the convergence of the Secant method to a locally unique solution of a nondifferentiable equation on a Banach space. Suppose x0, xâ1 are two initial points, and x1 is the first approximation generated by the Secant method. Our new idea uses the conditions â¥x1 â xiâ¥Â ⩽ η (i = 0, â1) instead of the classical conditions â¥x0 â xâ1â¥Â ⩽ α and â¥x1 â x0â¥Â ⩽ η. Finally, a numerical example is provided to show that our result applies, where earlier one fails.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Hongmin Ren,