2023•Вестник Российского университета дружбы народов. Серия: Математика, информатика, физикаOpen access

Convergence of the grid method for the Fredholm equation of the first kind with Tikhonov regularization

Aleksandr A. Belov

Abstract

The paper describes a grid method for solving an ill-posed problem for the Fredholm equation of the first kind using the A. N. Tikhonov regularizer. The convergence theorem for this method was formulated and proved. A procedure for thickening grids with a simultaneous increase in digit capacity of calculations is proposed.

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Key concepts: Tikhonov regularization, Fredholm integral equation, Regularization (linguistics), Grid, Convergence (economics), Mathematics, Integral equation, Applied mathematics