Partial Inverse Heuristic for the Approximate Solution of Non-linear Equations

摘要: We show how to generate many fix-point iterators of the form x i +1= F(x ) which could solve a given non-linear equation. In particular, these tend have good global convergence, and we examples whereby obscure solutions can be discovered. This methods are only suitable for computer algebra systems, where equations solved manipulated in symbolic form. Also, systematic method finding most or all nonlinear that multiple is described. The successful constructed small number occurrences F. use grouping polynomial terms expressions x, e using known inverse relations obtain better iterators. Each iterator tried limited way, expectation at least one them will succeed. heuristic shows very behaviour cases, particular when answer involves extreme ranges.