On two-dimensional shape-preserving approximation
Danylo Radchenko
TL;DR
This paper explores methods for approximating continuous functions with smooth functions that preserve shape by maintaining a nonnegative Jacobian, aiming to improve shape-preserving approximations.
Contribution
It introduces a new approach to approximate continuous mappings with smooth, shape-preserving functions, focusing on nonnegative Jacobian constraints.
Findings
Established conditions for shape-preserving approximation
Developed a method for smooth approximation with nonnegative Jacobian
Demonstrated effectiveness through theoretical analysis
Abstract
In this paper we investigate a problem of approximation of continuous mappings by smooth mappings with nonnegative Jacobian.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Analytic and geometric function theory · Advanced Numerical Analysis Techniques