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<p>This paper is motivated by a result obtained by Schulz in 1933 for computing an approximation to the inverse of a non-singular matrix. The algorithm by Schulz is quadratic convergent and we try to use it in producing a new inexact Newton method for the unconstrained optimization. We prove that this inexact Newton method is quadratic convergent and is faster than the Newton method with Cholesky factorization for solving large-scale unconstrained optimization problems.</p>

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A new inexact Newton method with the approximate to the inverse of the Hessian for the unconstrained optimization

  • 期刊论文

  • 发表日期：

    2026年1月23日

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  • Neculai Andrei

摘要

This paper is motivated by a result obtained by Schulz in 1933 for computing an approximation to the inverse of a non-singular matrix. The algorithm by Schulz is quadratic convergent and we try to use it in producing a new inexact Newton method for the unconstrained optimization. We prove that this inexact Newton method is quadratic convergent and is faster than the Newton method with Cholesky factorization for solving large-scale unconstrained optimization problems.