Elliptic Quadratic Operator Equations
Rasul Ganikhodjaev, Farrukh Mukhamedov, Mansoor Saburov
TL;DR
This paper investigates elliptic quadratic operator equations in finite-dimensional Euclidean spaces, establishing conditions for solutions and presenting an iterative method for stable solutions.
Contribution
It provides necessary and sufficient conditions for solutions and introduces an iterative Newton-Kantorovich method for stability analysis.
Findings
Derived conditions for existence of solutions
Presented an iterative method for stable solutions
Analyzed stability of solutions
Abstract
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Differential Equations and Boundary Problems · Matrix Theory and Algorithms