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

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 differ...

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Bibliographic Details
Published inCalcolo Vol. 62; no. 2
Main Authors Cao, Huiping, Li, Wugang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2025
Subjects
Mathematics
Mathematics and Statistics
Numerical Analysis
Theory of Computation
90C53
Diagonal quasi-Newton method
Nonlinear equations
65K05
Weak direct tangent condition
65H10
Local convergence
Automatic differentiation
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ISSN0008-0624
1126-5434
DOI10.1007/s10092-025-00645-0

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Summary: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.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-025-00645-0