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The article considers the discrete analogue of the method of quickest descentfor an inverse Acoustics problem in case of a smooth source. The authorsderived the gradient of functional in differential and discrete cases,described the algorithm of solving a problem, and compared gradients offunctional in continuous and discrete cases. In the article the improvedestimates of the rates of convergence of gradient-based methods are obtained,which are very important for practice because they provide with the possibilityto make input data errors consistent with the iteration number. There is apractical application of the proposed new method of deriving the gradient offunctional for an Acoustics discrete problem, for it provides with calculationsthat are more accurate. The theoretical importance of the method is thedeveloped technique of deriving estimates and gradients of functional at adiscrete level.

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