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Square root algorithms
Algorithms for calculating square roots
Square root algorithms
Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square roots of natural numbers, other than of perfect squares, are irrational, square roots can usually only be computed to some finite precision: these algorithms typically construct a series of increasingly accurate approximations. Most square root computation methods are iterative: after choosing a suitable initial estimate of S {\displaystyle {\sqrt {S}}} , an iterative refinement is performed until some termination criterion is met. One refinement option is Heron's method, a special case of Newton's method. If division is much more costly than multiplication, it may be preferable to compute the inverse square root instead...
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