Laguerre-like inclusion method for polynomial zeros
نویسندگان
چکیده
منابع مشابه
Laguerre-like Methods with Corrections for the Inclusion of Polynomial Zeros
Iterative methods of Laguerre’s type for the simultaneous inclusion of all zeros of a polynomial are proposed. Using Newton’s and Halley’s corrections, the order of convergence of the basic method is increased from 4 to 5 and 6, respectively. Further improvements are achieved by the Gauss-Seidel approach. Using the concept of the R-order of convergence of mutually dependent sequences, we presen...
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An improved iterative method of Euler’s type for the simultaneous inclusion of polynomial zeros is considered. To accelerate the convergence of the basic method of fourth order, Carstensen-Petković’s approach [7] using Weierstrass’ correction is applied. It is proved that the R-order of convergence of the improved Euler-like method is (asymptotically) 2 + √ 7 ≈ 4.646 or 5, depending of the type...
متن کاملLaguerre-like Methods for the Simultaneous Approximation of Polynomial Multiple Zeros
Two new methods of the fourth order for the simultaneous determination of multiple zeros of a polynomial are proposed. The presented methods are based on the fixed point relation of Laguerre's type and realized in ordinary complex arithmetic as well as circular complex interval arithmetic. The derived iterative formulas are suitable for the construction of modified methods with improved converg...
متن کاملCauchy-type Inclusion and Exclusion Regions for Polynomial Zeros
A classical result by Cauchy defines a disk containg all the zeros of a polynomial. We derive several related results by using similarity transformations of a polynomial’s companion matrix, together with Gershgorin’s theorem. We thus show that Cauchy’s original result can be seen as but one member of a family of related results. MathEduc Subject Classification: H35 MSC Subject Classification: 9...
متن کاملFilomat 17 (2003), 155–168 Derivative Free Combined Method for the Simultaneous Inclusion of Polynomial Zeros
Abstract. A combined method for the simultaneous inclusion of complex zeros of a polynomial, composed of two circular arithmetic methods, is presented. This method does not use polynomial derivatives and has the order of convergence equals four. Computationally verifiable initial conditions that guarantee the convergence are also stated. Two numerical example are included to demonstrate the con...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(02)00723-9