Multidimensional moment problem and diagonal Schur algorithm
Ivan Kovalyov
TL;DR
This paper investigates the multidimensional moment problem using Steiltjes transforms, introduces a diagonal algorithm for solving it, and characterizes solutions via continued fractions, also addressing truncated cases.
Contribution
It presents a novel diagonal step-by-step algorithm for the multidimensional moment problem and characterizes all solutions through continued fractions.
Findings
The algorithm effectively solves the full multidimensional moment problem.
Solutions are explicitly described using continued fractions.
The method applies to both full and truncated multidimensional moment problems.
Abstract
The multidimensional moment problem is studied in terms of the Steiltjes transform. The diagonal step-by-step algorithm is constructed for the multidimensional moment problem. The set of solutions of the full multidimensional moment problem is found in terms of the continued fractions. Moreover, the diagonal step-by-step algorithm can be applied to the special truncated multidimensional moment problem.
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Taxonomy
TopicsMetaheuristic Optimization Algorithms Research · Data Management and Algorithms · Optimization and Search Problems