<p>A new class of diagonal quasi-Newton method for solving large-scale nonlinear equations is discussed in this paper. We first introduce a weak direct tangent condition, which can be viewed as a projection of the direct tangent condition along the step direction and can be computed by automatic differentiation. Then the diagonal approximation matrix is determined by the least change principle and weak direct tangent condition. Under suitable assumptions, the proposed diagonal quasi-Newton method is proved to be locally and linearly convergent on the basis of the bounded deterioration property. Subject to the CPU time and number of iterations, intensive numerical experiments show that the diagonal quasi-Newton method based on automatic differentiation performs better than Newton’s method and Broyden’s method, respectively.</p>

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A diagonal quasi-Newton method based on automatic differentiation for nonlinear equations

  • Huiping Cao,
  • Wugang Li

摘要

A new class of diagonal quasi-Newton method for solving large-scale nonlinear equations is discussed in this paper. We first introduce a weak direct tangent condition, which can be viewed as a projection of the direct tangent condition along the step direction and can be computed by automatic differentiation. Then the diagonal approximation matrix is determined by the least change principle and weak direct tangent condition. Under suitable assumptions, the proposed diagonal quasi-Newton method is proved to be locally and linearly convergent on the basis of the bounded deterioration property. Subject to the CPU time and number of iterations, intensive numerical experiments show that the diagonal quasi-Newton method based on automatic differentiation performs better than Newton’s method and Broyden’s method, respectively.