Enclosing roots of polynomial equations and their applications to iterative processes
We introduce a special class of real recurrentpolynomials f<SUB>n</SUB> (n ≥ 1) of degree n,with unique positive roots s<SUB>n</SUB>, which are decreasingas n increases. The first root s<SUB>1</SUB>, as well asthe last one denoted by s<SUB>∞</SUB> are...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2009-11-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | http://www.utgjiu.ro/math/sma/v04/p10.pdf |
| Summary: | We introduce a special class of real recurrentpolynomials f<SUB>n</SUB> (n ≥ 1) of degree n,with unique positive roots s<SUB>n</SUB>, which are decreasingas n increases. The first root s<SUB>1</SUB>, as well asthe last one denoted by s<SUB>∞</SUB> are expressed in closedform, and enclose all s<SUB>n</SUB> (n > 1). <BR>This technique is also used to find weaker than before[Kantorovich and Akilov, 1982] sufficient convergence conditions for some popular iterative processes converging to solutions of equations. |
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| ISSN: | 1843-7265 1842-6298 |