ニュートン法

newton.pl

#!/usr/bin/env perl

use strict;
use warnings;
use feature 'say';

use DDP { deparse => 1 };

print "求めたい平方根を入力>>";
chomp(my $root_num = <STDIN>);

my $x= 3;
my $delta_limit = 0.0000001;
my $new_x = calc_point($x);

while ($x - $new_x > $delta_limit){
    $x = $new_x;
    $new_x = calc_point($x);
}
 say $new_x;

sub calc_point{
    my $i = shift;
    my $mo = 2 * $i;
    my $chi = ($i ** 2 - $root_num);
    my $result = $i - $chi / $mo;
    return $result;
}
__END__

memo

f(x) = x^2 - $root_num;
f(x) = 0;

f'(x) = 2x;
f'(x0) = 2x0;

f'(x0) = f(x0) / x0 - x1

2x0 = f(x0) / x0 - x1

f(x0) = x0^2 - root_num

2x0 = x0^2 - root_num / x0 - x1
x0 - x1 = x0^2 - root_num / 2x0
- x1 = x0^2 - root_num / 2x0 - x0
x1 = - (x0^2 - root_num / 2x0) + x0