Steffensen's method: Difference between revisions
Added C++
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Line 287:
t0 += 0.1;
}
return 0;
}</syntaxhighlight>
Line 302 ⟶ 303:
t0 = 0.9 : intersection at (-0.681025, 2.681025)
t0 = 1.0 : no answer
</pre>
=={{header|C++}}==
{{trans|C}}
<syntaxhighlight lang="cpp">#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
double aitken(double (*f)(double), double p0) {
double p1 = f(p0);
double p2 = f(p1);
double p1m0 = p1 - p0;
return p0 - p1m0 * p1m0 / (p2 - 2.0 * p1 + p0);
}
double steffensenAitken(double (*f)(double), double pinit, double tol, int maxiter) {
double p0 = pinit;
double p = aitken(f, p0);
int iter = 1;
while (fabs(p - p0) > tol && iter < maxiter) {
p0 = p;
p = aitken(f, p0);
++iter;
}
if (fabs(p - p0) > tol) return nan("");
return p;
}
double deCasteljau(double c0, double c1, double c2, double t) {
double s = 1.0 - t;
double c01 = s * c0 + t * c1;
double c12 = s * c1 + t * c2;
return s * c01 + t * c12;
}
double xConvexLeftParabola(double t) {
return deCasteljau(2.0, -8.0, 2.0, t);
}
double yConvexRightParabola(double t) {
return deCasteljau(1.0, 2.0, 3.0, t);
}
double implicitEquation(double x, double y) {
return 5.0 * x * x + y - 5.0;
}
double f(double t) {
double x = xConvexLeftParabola(t);
double y = yConvexRightParabola(t);
return implicitEquation(x, y) + t;
}
int main() {
double t0 = 0.0, t, x, y;
int i;
for (i = 0; i < 11; ++i) {
cout << "t0 = " << setprecision(1) << t0 << " : ";
t = steffensenAitken(f, t0, 0.00000001, 1000);
if (isnan(t)) {
cout << "no answer << endl;
} else {
x = xConvexLeftParabola(t);
y = yConvexRightParabola(t);
if (fabs(implicitEquation(x, y)) <= 0.000001) {
cout << "intersection at (" << x << ", " << y << ")" << endl;
} else {
cout << "spurious solution" << endl;
}
}
t0 += 0.1;
}
return 0;
}</syntaxhighlight>
{{out}}
<pre>
Same as C example.
</pre>
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