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Methods of computing square roots are algorithms for approximating the non-negative square root of a positive real number. Since all square roots of natural numbers , other than of perfect squares , are irrational , [1] square roots can usually only be computed to some finite precision: these methods typically construct a series of increasingly ...
Use of Newton's method to compute square roots. Newton's method is one of many known methods of computing square roots. Given a positive number a, the problem of finding a number x such that x2 = a is equivalent to finding a root of the function f(x) = x2 − a. The Newton iteration defined by this function is given by.
In mathematics, Bhāskara I's sine approximation formula is a rational expression in one variable for the computation of the approximate values of the trigonometric sines discovered by Bhāskara I (c. 600 – c. 680), a seventh-century Indian mathematician. [1] This formula is given in his treatise titled Mahabhaskariya.
A few steps of the bisection method applied over the starting range [a 1 ;b 1 ]. The bigger red dot is the root of the function. In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval ...
The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.
Fast inverse square root, sometimes referred to as Fast InvSqrt () or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in IEEE 754 floating-point format. The algorithm is best known for its implementation in 1999 in Quake III ...
Secant method. In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method. However, the secant method predates Newton's method by over 3000 years.
Halley's method. In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's ...