Sometimes Newton's Method Always Cycles
| Autor: | Joe Latulippe, Jennifer Switkes |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | The College Mathematics Journal. 43:365-370 |
| ISSN: | 1931-1346 0746-8342 |
| DOI: | 10.4169/college.math.j.43.5.365 |
| Popis: | SummaryAre there functions for which Newton's method cycles for all non-trivial initial guesses? We construct and solve a differential equation whose solution is a real-valued function that two-cycles under Newton iteration. Higher-order cycles of Newton's method iterates are explored in the complex plane using complex powers of x. We find a class of complex powers that cycle for all non-trivial initial guesses and present the results analytically and graphically. |
| Databáze: | OpenAIRE |
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