An analytic approach to the solution of non-linear equations (Q1096327)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: An analytic approach to the solution of non-linear equations |
scientific article; zbMATH DE number 4030819
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An analytic approach to the solution of non-linear equations |
scientific article; zbMATH DE number 4030819 |
Statements
An analytic approach to the solution of non-linear equations (English)
0 references
1987
0 references
The author [North-Holland Math. Stud. 110, 207-215 (1985; Zbl 0599.65028)] proposed an algorithm for the isolation of the zeros of a scalar analytic function which is based on tracing the zero curves of its real and imaginary parts. The algorithm is linear with respect to the exploration of the complex plane. In Section 1 of the present paper some numerical results for test polynomials are given. The main result in Section 2 is that the number of critical points is a branch region of order m equals m-1. In the earlier paper it was shown that in exceptional cases the tracing is not complete. Then the ``completeness algorithm'' was implemented. This algorithm is analyzed in Section 3 of the present paper.
0 references
polynomial zeros
0 references
zero curve tracing
0 references
function structure
0 references
graphical display
0 references
regions of univalence
0 references
listprocessing
0 references
numerical examples
0 references
isolation of zeros
0 references
analytic function
0 references
critical points
0 references
branch region
0 references
