Die Sekantenmethode wird verwendet, um die Wurzel einer Gleichung f(x) = 0 zu finden. Sie beginnt mit zwei unterschiedlichen Schätzungen x1 und x2 für die Wurzel. Es handelt sich um ein iteratives Verfahren mit linearer Interpolation bis zu einer Wurzel. Die Iteration stoppt, wenn die Differenz zwischen zwei Zwischenwerten kleiner als der Konvergenzfaktor ist.
Beispiele:
Eingabe: Gleichung = x3+ x - 1
x1 = 0 x2 = 1 E = 0,0001
Ausgabe : Wurzel der gegebenen Gleichung = 0,682326
Anzahl der Iterationen = 5
Algorithmus
Initialize: x1 x2 E n // E = convergence indicator calculate f(x1)f(x2) if(f(x1) * f(x2) = E); //repeat the loop until the convergence print 'x0' //value of the root print 'n' //number of iteration } else print 'can not found a root in the given interval'C++
// C++ Program to find root of an // equations using secant method #include using namespace std; // function takes value of x and returns f(x) float f(float x) { // we are taking equation as x^3+x-1 float f = pow(x 3) + x - 1; return f; } void secant(float x1 float x2 float E) { float n = 0 xm x0 c; if (f(x1) * f(x2) < 0) { do { // calculate the intermediate value x0 = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1)); // check if x0 is root of equation or not c = f(x1) * f(x0); // update the value of interval x1 = x2; x2 = x0; // update number of iteration n++; // if x0 is the root of equation then break the loop if (c == 0) break; xm = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1)); } while (fabs(xm - x0) >= E); // repeat the loop // until the convergence cout << 'Root of the given equation=' << x0 << endl; cout << 'No. of iterations = ' << n << endl; } else cout << 'Can not find a root in the given interval'; } // Driver code int main() { // initializing the values float x1 = 0 x2 = 1 E = 0.0001; secant(x1 x2 E); return 0; }
Java // Java Program to find root of an // equations using secant method class GFG { // function takes value of x and // returns f(x) static float f(float x) { // we are taking equation // as x^3+x-1 float f = (float)Math.pow(x 3) + x - 1; return f; } static void secant(float x1 float x2 float E) { float n = 0 xm x0 c; if (f(x1) * f(x2) < 0) { do { // calculate the intermediate // value x0 = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1)); // check if x0 is root of // equation or not c = f(x1) * f(x0); // update the value of interval x1 = x2; x2 = x0; // update number of iteration n++; // if x0 is the root of equation // then break the loop if (c == 0) break; xm = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1)); // repeat the loop until the // convergence } while (Math.abs(xm - x0) >= E); System.out.println('Root of the' + ' given equation=' + x0); System.out.println('No. of ' + 'iterations = ' + n); } else System.out.print('Can not find a' + ' root in the given interval'); } // Driver code public static void main(String[] args) { // initializing the values float x1 = 0 x2 = 1 E = 0.0001f; secant(x1 x2 E); } } // This code is contributed by Anant Agarwal.
Python3 # Python3 Program to find root of an # equations using secant method # function takes value of x # and returns f(x) def f(x): # we are taking equation # as x^3+x-1 f = pow(x 3) + x - 1; return f; def secant(x1 x2 E): n = 0; xm = 0; x0 = 0; c = 0; if (f(x1) * f(x2) < 0): while True: # calculate the intermediate value x0 = ((x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1))); # check if x0 is root of # equation or not c = f(x1) * f(x0); # update the value of interval x1 = x2; x2 = x0; # update number of iteration n += 1; # if x0 is the root of equation # then break the loop if (c == 0): break; xm = ((x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1))); if(abs(xm - x0) < E): break; print('Root of the given equation =' round(x0 6)); print('No. of iterations = ' n); else: print('Can not find a root in ' 'the given interval'); # Driver code # initializing the values x1 = 0; x2 = 1; E = 0.0001; secant(x1 x2 E); # This code is contributed by mits
C# // C# Program to find root of an // equations using secant method using System; class GFG { // function takes value of // x and returns f(x) static float f(float x) { // we are taking equation // as x^3+x-1 float f = (float)Math.Pow(x 3) + x - 1; return f; } static void secant(float x1 float x2 float E) { float n = 0 xm x0 c; if (f(x1) * f(x2) < 0) { do { // calculate the intermediate // value x0 = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1)); // check if x0 is root of // equation or not c = f(x1) * f(x0); // update the value of interval x1 = x2; x2 = x0; // update number of iteration n++; // if x0 is the root of equation // then break the loop if (c == 0) break; xm = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1)); // repeat the loop until // the convergence } while (Math.Abs(xm - x0) >= E); Console.WriteLine('Root of the' + ' given equation=' + x0); Console.WriteLine('No. of ' + 'iterations = ' + n); } else Console.WriteLine('Can not find a' + ' root in the given interval'); } // Driver code public static void Main(String []args) { // initializing the values float x1 = 0 x2 = 1 E = 0.0001f; secant(x1 x2 E); } } // This code is contributed by vt_m.
PHP // PHP Program to find root of an // equations using secant method // function takes value of x // and returns f(x) function f( $x) { // we are taking equation // as x^3+x-1 $f = pow($x 3) + $x - 1; return $f; } function secant($x1 $x2 $E) { $n = 0; $xm; $x0; $c; if (f($x1) * f($x2) < 0) { do { // calculate the intermediate value $x0 = ($x1 * f($x2) - $x2 * f($x1)) / (f($x2) - f($x1)); // check if x0 is root // of equation or not $c = f($x1) * f($x0); // update the value of interval $x1 = $x2; $x2 = $x0; // update number of iteration $n++; // if x0 is the root of equation // then break the loop if ($c == 0) break; $xm = ($x1 * f($x2) - $x2 * f($x1)) / (f($x2) - f($x1)); // repeat the loop // until the convergence } while (abs($xm - $x0) >= $E); echo 'Root of the given equation='. $x0.'n' ; echo 'No. of iterations = '. $n ; } else echo 'Can not find a root in the given interval'; } // Driver code { // initializing the values $x1 = 0; $x2 = 1; $E = 0.0001; secant($x1 $x2 $E); return 0; } // This code is contributed by nitin mittal. ?> JavaScript <script> // JavaScript Program to find root of an // equations using secant method // function takes value of x and returns f(x) function f(x) { // we are taking equation as x^3+x-1 let f = Math.pow(x 3) + x - 1; return f; } function secant(x1 x2 E) { let n = 0 xm x0 c; if (f(x1) * f(x2) < 0) { do { // calculate the intermediate value x0 = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1)); // check if x0 is root of equation or not c = f(x1) * f(x0); // update the value of interval x1 = x2; x2 = x0; // update number of iteration n++; // if x0 is the root of equation then break the loop if (c == 0) break; xm = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1)); } while (Math.abs(xm - x0) >= E); // repeat the loop // until the convergence document.write('Root of the given equation=' + x0.toFixed(6) + '
'); document.write('No. of iterations = ' + n + '
'); } else document.write('Can not find a root in the given interval'); } // Driver code // initializing the values let x1 = 0 x2 = 1 E = 0.0001; secant(x1 x2 E); // This code is contributed by Surbhi Tyagi. </script>
Zeitkomplexität: O(1)
Hilfsraum: O(1)
Referenz
https://en.wikipedia.org/wiki/Secant_method