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Abstract <p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • B. I. Valiakhmetov,
  • D. V. Lukyanenko,
  • E. E. Tyrtyshnikov

摘要

Abstract

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.