Journal of Applied Mathematics and Computation

DOI：http://dx.doi.org/10.26855/jamc.2023.03.021

Date: May 6,2023 Hits: 213

In this paper, we treat an ill-posed problem for the determination of an unknown source in the Poisson equation. We make a theoretical analysis of the approximation of the function (A)g = (I −e ^{−A}) ^{−1}A^{2}g by using the Krylov subspace me-thod, and we derive some error estimates. The idea is to project the approximate operator (I − e ^{−A}) ^{−1}A^{ 2} on a small subspace, and perform matrix calculations that result. Having good estimates or even bounds for the error in computing approximations to expression of the *f(A)v* is very important in pratical application. This opportunity is for us to propose a basic approach to solving the inverse problem, then estimate the error to see its effectiveness and the convergence of the solution. This general approach, which has been used with success in several applications, provides a systematic way of defining high order explicit-type schemes for solving of Poisson equation.

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**Error Bounds for Krylov Approximation and Exact Solution of Identifying an Unknown Source in the Poisson Equation**

**How to cite this paper:** Ousmane Samba Coulibaly, Boureima Sangaré. (2023) Error Bounds for Krylov Approximation and Exact Solution of Identifying an Unknown Source in the Poisson Equation. *Journal of Applied Mathematics and Computation*, **7**(**1**), 188-201.

**DOI: http://dx.doi.org/10.26855/jamc.2023.03.021**

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