“Laguerre's Method”的概念、定义、习题解题方法及翻译-数学辞典

单词

Laguerre's Method

释义

Laguerre's Method

A Root-finding algorithm which converges to a Complex Root from any starting position.

(1)

(2)


			(3)


			(4)


			(5)

Now let

and

. Then

(6)

(7)

(8)

Setting

gives Halley's Irrational Formula.

See also Halley's Irrational Formula, Halley's Method, Newton's Method, Root

References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 365-366, 1992.

Ralston, A. and Rabinowitz, P. §8.9-8.13 in A First Course in Numerical Analysis, 2nd ed. New York: McGraw-Hill, 1978.

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