What question did this study set out to answer?

To develop an efficient preconditioner for accelerating solutions to linear algebraic equations in inverse problems.

February 23, 2026

Acceleration of Iterative Methods for Solving Linear Inverse Problems Based on Low-Rank Approximation

Puntos clave

To develop an efficient preconditioner for accelerating solutions to linear algebraic equations in inverse problems.
Constructed a preconditioner based on low-rank approximation of the system matrix
Applied the method to systems of linear algebraic equations
Evaluated computational efficiency in the context of inverse problems
Reduced the number of iterations required for convergence in iterative methods
Demonstrated significant computational resource savings in processing experimental data
Enhanced accuracy in the reconstruction of measured quantities

Resumen

An efficient method is proposed for constructing a preconditioner for accelerated solution of systems of linear algebraic equations arising in solving linear inverse problems. The method relies on the properties of a low-rank approximation of the original system matrix and allows for a significant reduction in the number of iterations in iterative solution methods. Significant savings in computational resources can be achieved in the inverse problem of processing experimental data measured in a spatial domain separated from the domain of localization of the quantities to be reconstructed.

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