Standard Kantorovich theorem of the Chebyshev method on complex plane. (English) Zbl 0747.65030
After redefining the Chebyshev method the author presents a Kantorovich type convergence theorem including lower and upper bounds. The proof which is said to use analysis techniques is omitted but the paper contains a detailed list of references for further readings.
Reviewer: H.Kriete (Bochum)
MSC:
| 65H05 | Numerical computation of solutions to single equations |
| 65E05 | General theory of numerical methods in complex analysis (potential theory, etc.) |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
Keywords:
polynomial equations; Chebyshev method; Kantorovich type convergence theorem; lower and upper boundsReferences:
| [1] | DOI: 10.1080/00207168908803697 · Zbl 0667.65041 · doi:10.1080/00207168908803697 |
| [2] | DOI: 10.1080/00207169008803805 · Zbl 0751.65032 · doi:10.1080/00207169008803805 |
| [3] | DOI: 10.1080/00207169008803802 · Zbl 0751.65031 · doi:10.1080/00207169008803802 |
| [4] | Chen Dong, Intern. J. Computer Math 31 (1990) |
| [5] | Chen Dong, Intern. J. Computer Math 31 (1990) |
| [6] | Chen Dong, Intern. J. Computer Math 31 (1990) |
| [7] | Traub J.F., Iterative Methods for the Solution of Equations (1964) · Zbl 0121.11204 |
| [8] | Werner W., Lecture Notes in Math 878 (1980) |
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