自编二分法、简单迭代法、牛顿法、Aitken法、弦割法求方程

#include "iteration.h" #define FAILURE -1 double Dichotomy( double a, double b, double (*fun)(double), double epsinon ) { double x; unsigned counter = 0; if ( a > b ) { double c = a; a = b; b = c; } printf("二分法\n"); do { x = (a + b) / 2.0; if ( (*fun)(a) * (*fun)(x) < 0 ) { b = x; } else { a = x; } counter++; printf("第%d次迭代:", counter); printf(" x = %lf\n", x); } while ( b - a >= epsinon ); return x; } double Simple_Iterate( double x0, double (*Fi)(double), double epsinon ) { double New = x0; double Old; unsigned counter = 0; printf("简单迭代法\n"); do { Old = New; New = (*Fi)(Old); if ( fabs( (*Fi)(New) - New ) >= fabs( New - Old ) ) { return FAILURE; } counter++; printf("第%d次迭代:", counter); printf(" x = %lf\n", New); } while (fabs( New - Old ) >= epsinon); return New; } double Aitken( double x0, double (*Fi)(double), double epsinon ) { double xk, xk1_, xk1__, xk1; xk1 = x0; unsigned counter = 0; printf("Aitken法\n"); do { xk = xk1; xk1_ = (*Fi)(xk); xk1__ = (*Fi)(xk1_); xk1 = xk1__ - (( xk1__ - xk1_ ) * ( xk1__ - xk1_ ) ) / (xk1__ - 2 * xk1_ + xk ); counter++; printf("第%d次迭代:", counter); printf(" x = %lf\n", xk1); } while ( fabs( xk1 - xk ) >= epsinon ); return xk1; } double Newton( double x0, double (*Fun)(double), double (*Fun_)(double), double epsinon, unsigned M ) { double xk, xk1, f; unsigned counter = 0; xk1 = x0; printf("Newton法\n"); do { xk = xk1; if ( counter > M ) { return FAILURE; } f = (*Fun_)(xk); if ( f == 0 ) { return FAILURE; } xk1 = xk - (*Fun)(xk) / f; counter++; printf("第%d次迭代:", counter); printf(" x = %lf\n", xk1); } while ( fabs(xk1 - xk ) >= epsinon ); return xk1; } double XianGe( double x0, double x1, double (*Fun)(double), double epsinon, unsigned M ) { double xk_1, xk, xk1; unsigned counter = 0; xk = x0; xk1 = x1; printf("弦割法\n"); do { xk_1 = xk; xk = xk1; if ( counter > M ) {return FAILURE;} xk1 = xk - (*Fun)(xk) / ((*Fun)(xk) - (*Fun)(xk_1)) * (xk - xk_1); counter++; printf("第%d次迭代:", counter); printf(" x = %lf\n", xk1); } while ((fabs(xk1 - xk) >= epsinon ) ); return xk1; } double XiaShan( double x0, double (*Fun)(double), double (*Fun_)(double), double epsinon0, double epsinon, unsigned M ) { double x1, eps = 1; unsigned counter = 0; do { if ( eps < epsinon0 ) { return FAILURE; } if ( counter > M ) { return FAILURE; } eps = eps / 2; double f = (*Fun_)(x0); if ( f == 0 ) { return FAILURE; } x1 = x0 - (*Fun)(x0) / f; counter++; } while ( fabs((*Fun)(x1)) < fabs((*Fun)(x0)) ); return Newton( x0, (*Fun), (*Fun_), epsinon, M ); }