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- Nth_root_algorithm abstract "The principal nth root of a positive real number A, is the positive real solution of the equation(for integer n there are n distinct complex solutions to this equation if , but only one is positive and real).There is a very fast-converging nth root algorithm for finding Make an initial guess Set . In practice we do .Repeat step 2 until the desired precision is reached, i.e. .A special case is the familiar square-root algorithm. By setting n = 2, the iteration rule in step 2 becomes the square root iteration rule:Several different derivations of this algorithm are possible. One derivation shows it is a special case of Newton's method (also called the Newton-Raphson method) for finding zeros of a function beginning with an initial guess. Although Newton's method is iterative, meaning it approaches the solution through a series of increasingly accurate guesses, it converges very quickly. The rate of convergence is quadratic, meaning roughly that the number of bits of accuracy doubles on each iteration (so improving a guess from 1 bit to 64 bits of precision requires only 6 iterations). For this reason, this algorithm is often used in computers as a very fast method to calculate square roots.For large n, the nth root algorithm is somewhat less efficient since it requires the computation of at each step, but can be efficiently implemented with a good exponentiation algorithm.".
- Nth_root_algorithm wikiPageID "1620000".
- Nth_root_algorithm wikiPageRevisionID "592152069".
- Nth_root_algorithm hasPhotoCollection Nth_root_algorithm.
- Nth_root_algorithm subject Category:Root-finding_algorithms.
- Nth_root_algorithm type Abstraction100002137.
- Nth_root_algorithm type Act100030358.
- Nth_root_algorithm type Activity100407535.
- Nth_root_algorithm type Algorithm105847438.
- Nth_root_algorithm type Event100029378.
- Nth_root_algorithm type Procedure101023820.
- Nth_root_algorithm type PsychologicalFeature100023100.
- Nth_root_algorithm type Root-findingAlgorithms.
- Nth_root_algorithm type Rule105846932.
- Nth_root_algorithm type YagoPermanentlyLocatedEntity.
- Nth_root_algorithm comment "The principal nth root of a positive real number A, is the positive real solution of the equation(for integer n there are n distinct complex solutions to this equation if , but only one is positive and real).There is a very fast-converging nth root algorithm for finding Make an initial guess Set . In practice we do .Repeat step 2 until the desired precision is reached, i.e. .A special case is the familiar square-root algorithm.".
- Nth_root_algorithm label "Algorithme de calcul de la racine n-ième".
- Nth_root_algorithm label "Algorytm obliczania pierwiastka n-tego stopnia".
- Nth_root_algorithm label "Nth root algorithm".
- Nth_root_algorithm label "Алгоритм нахождения корня n-ной степени".
- Nth_root_algorithm sameAs Algorithme_de_calcul_de_la_racine_n-ième.
- Nth_root_algorithm sameAs Algorytm_obliczania_pierwiastka_n-tego_stopnia.
- Nth_root_algorithm sameAs m.05h7sr.
- Nth_root_algorithm sameAs Q2835826.
- Nth_root_algorithm sameAs Q2835826.
- Nth_root_algorithm sameAs Nth_root_algorithm.
- Nth_root_algorithm wasDerivedFrom Nth_root_algorithm?oldid=592152069.
- Nth_root_algorithm isPrimaryTopicOf Nth_root_algorithm.