总结求平方根sqrt的三种方法，首先是牛顿迭代法：functionabs{returnx>=0?search:error;}console.log;>2.23602294921875最后是“不动点方程”：functionabs{returnx>=0?next:try_with;}returntry_with;}functionaverage(x,y){return/2;}functionsqrt{returnfixed_point;}sqrt;以上为三种求“平方根”的方法。
总结求平方根sqrt的三种方法，首先是牛顿迭代法：
function abs(x) {return x >= 0 ? x : -x;}function square(x) {return x * x;}function good_enough(guess, x) {return abs(square(guess) - x) < 0.001;}function average(x, y) {return (xy) / 2;}function improve(guess, x) {return average(guess, x / guess);}function sqrt_iter(guess, x) {return good_enough(guess, x) ? guess : sqrt_iter(improve(guess, x), x);}function sqrt(x) {return sqrt_iter(1, x);}sqrt(5);> 2.2360688956433634
其次是二分法：
function average(x, y) {return (xy) / 2;}function positive(x) { return x > 0; }function negative(x) { return x < 0; }function abs(x) {return x >= 0 ? x : -x;}function close_enough(x, y) {return abs(x - y) < 0.001;}function search(f, neg_point, pos_point) {let midpoint = average(neg_point, pos_point);if (close_enough(neg_point, pos_point)) {return midpoint;} else {let test_value = f(midpoint);if (positive(test_value)) {return search(f, neg_point, midpoint);} else if (negative(test_value)) {return search(f, midpoint, pos_point);} else {return midpoint;}}}function binary_search_method(f, a, b) {let a_value = f(a);let b_value = f(b);return negative(a_value) && positive(b_value) ? search(f, a, b) : negative(b_value) && positive(a_value) ? search(f, b, a) : error("values are not of opposite sign");}console.log(binary_search_method(x => x ** 2- 5, 0, 5));>2.23602294921875
最后是“不动点方程”：
function abs(x) {return x >= 0 ? x : -x;}const tolerance = 0.00001;function fixed_point(f, first_guess) {function close_enough(x, y) {return abs(x - y) < tolerance;}function try_with(guess) {const next = f(guess);return close_enough(guess, next)? next: try_with(next);}return try_with(first_guess);}function average(x, y) {return (xy) / 2;}function sqrt(x) {return fixed_point(y => average(y, x / y), 1);}sqrt(5);
以上为三种求“平方根”的方法。
