Computer Methods for Mathematical Computations
Computer Methods for Mathematical Computations
Sorting-Based Calculation of Zeroes and Extrema of Functions as Applied to Search and Recognition. I
Cybernetics and Systems Analysis
Sorting-Based Calculation of Zeros and Extrema of Functions as Applied to Search and Recognition. II
Cybernetics and Systems Analysis
Sorting-based localization and stable computation of zeros of a polynomial. II
Cybernetics and Systems Analysis
Numerical sorting-based optimization as applied to general differential and nonlinear equations
Cybernetics and Systems Analysis
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A method of stable address sorting is designed for localization and approximate computation of real and complex zeros of a polynomial. In an arbitrary domain, a software implementation of the method allows one to localize and to calculate with high accuracy all zeros of a polynomial, including the case when they are ill-separated. The vicinity of each zero dynamically decreases during localizing the boundaries of the domains of all zeros. Algorithms developed are formally described in the Object Pascal language and are implemented in the Delphi 7 environment. Some upper-bound estimates of a parallel version of the method are given.