An Etymological Dictionary of Astronomy and Astrophysics

English-French-Persian

فرهنگ ریشه‌شناختی اخترشناسی-اخترفیزیک

Homepage  Preliminaries  Abbreviations  Acknowledgments  References 
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Newton-Raphson method
  روش ِ نیوتن-رفسون  
raveš-e Newton-Raphson
Fr.: méthode de Newton-Raphson  

A method for finding roots of a → polynomial that makes explicit use of the → derivative of the function. It uses → iteration to continually improve the accuracy of the estimated root.

If f(x) has a → simple root near xn then a closer estimate to the root is xn + 1</SUB where xn + 1</SUB = xn - f(xn)/f’(xn).
The iteration begins with an initial estimate of the root, x0, and continues to find x1, x2, . . . until a suitably accurate estimate of the position of the root is obtained. Also called → Newton’s method.

See also: → Newton found the method in 1671, but it was not actually published until 1736;
Joseph Raphson (1648-1715), English mathematician, independently published the method in 1690.