The discrete analogue of the method of quickest descent for an inverse acoustic problem in case of a smooth source

TL;DR

This paper develops a discrete analogue of the quickest descent method for inverse acoustic problems with smooth sources, providing improved gradient calculations and convergence estimates for practical and theoretical advancements.

Contribution

It introduces a new discrete method for gradient calculation in inverse acoustics problems, enhancing accuracy and convergence analysis compared to continuous approaches.

Findings

Derived the gradient of the functional in discrete and differential cases.

Provided improved convergence rate estimates for gradient-based methods.

Demonstrated practical accuracy improvements in inverse acoustics calculations.

Abstract

The article considers the discrete analogue of the method of quickest descent for an inverse Acoustics problem in case of a smooth source. The authors derived the gradient of functional in differential and discrete cases, described the algorithm of solving a problem, and compared gradients of functional in continuous and discrete cases. In the article the improved estimates of the rates of convergence of gradient-based methods are obtained, which are very important for practice because they provide with the possibility to make input data errors consistent with the iteration number. There is a practical application of the proposed new method of deriving the gradient of functional for an Acoustics discrete problem, for it provides with calculations that are more accurate. The theoretical importance of the method is the developed technique of deriving estimates and gradients of functional at a discrete level.