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Cubic convergence of parameter-controlled Newton-secant method for multiple zeros

โœ Scribed by Young Hee Geum; Young Ik Kim

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
524 KB
Volume
233
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

Let f : C โ†’ C have a multiple zero ฮฑ with integer multiplicity m โ‰ฅ 1 and be analytic in a sufficiently small neighborhood of ฮฑ. For parameter-controlled Newton-secant method defined by

we investigate the maximal order of convergence and the theoretical asymptotic error constant by seeking the relationship between parameters ฮป and ยต. For various test functions, the numerical method has shown a satisfactory result with high-precision Mathematica programming.

๐Ÿ“œ SIMILAR VOLUMES

On Newton-type methods for multiple root
On Newton-type methods for multiple roots with cubic convergence
โœ H.H.H. Homeier ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 374 KB

## a b s t r a c t We introduce two families of Newton-type methods for multiple roots with cubic convergence. A further Newton-type method for multiple roots with cubic convergence is presented that is related to quadrature. We also provide numerical tests that show that these new methods are comp