false-position Algorithm
In mathematics, the regula falsi, method of false position, or false position method is a very old method for solve an equation in one unknown, that, in modify form, is still in purpose. In simple terms, the method is the trial and mistake technique of use test (The simple false position technique is found in cuneiform tablets from ancient Babylonian mathematics, and in papyri from ancient Egyptian mathematics.
Within the tradition of medieval Muslim mathematics, double false position was known as hisāb al-khaṭāʾayn (" reckoning by two errors").Regula Falsi looks as the Latinized version of rule of false as early as 1690.Several 16th century European writers feel the need to apologize for the name of the method in a science that seeks to find the truth.
#include<stdlib.h>
#include <math.h>
#include <iostream>
float eq(float i) {
return (pow(i, 3) - (4 * i) - 9); // origial equation
}
int main() {
float a, b, z, c, m, n;
system("clear");
for (int i = 0; i < 100; i++) {
z = eq(i);
if (z >= 0) {
b = i;
a = --i;
goto START;
}
}
START:
std::cout << "\nFirst initial: " << a;
std::cout << "\nSecond initial: " << b;
for (int i = 0; i < 100; i++) {
float h, d;
m = eq(a);
n = eq(b);
c = ((a * n) - (b * m)) / (n - m);
a = c;
z = eq(c);
if (z > 0 && z < 0.09) { // stoping criteria
goto END;
}
}
END:
std::cout << "\n\nRoot: " << c;
system("pause");
}
