The Gauss–Newton–Broyden method is proposed and investigated for solving a nonlinear least squares problem with operator decomposition. This method is obtained from the Gauss–Newton method by replacing the Jacobian matrix of a nonlinear operator with the sum of the derivative of the differentiable part of the operator and the matrix computed by the Broyden update formula for the other part of the nonlinear vector function. A local convergence theorem for the proposed method, under the classical Lipschitz conditions and for problems with zero residual, is proved. The results of numerical experiments are also presented.
This paper considers the local convergence for solving general nonlinear equations. We establish randomized quasi-Gauss--Newton methods based on the approximation of the Gram matrix, addressing both the underdetermined and the overdetermined settings. For the underdetermined case, we show that our methods achieve local...
We study the quasi-Newton method by using set-valued approximations for solving generalized equations without smoothness assumptions. The set-valued approximations appear naturally when dealing with nonsmooth problems, or even in smooth cases, data in almost concrete applications are not exact. We present a generalizat...
Samir Adly, Ngai van Huynh· Journal of Convex Analysis· 6 citations
This paper is concerned with the linear approximation method (i.e. the iterative method in which a sequence of vectors is generated by solving certain linearized subproblems) for solving the variational inequality. The global convergent iterative process is proposed by applying the continuation method, and the related...
Zhao-Yong You, Si-Quan Zhu· Journal of Computational Mat...· 1 citation
We analyze a least-squares asymmetric radial basis function
collocation method for solving the modified Helmholtz equations. In
the theoretical part, we proved the convergence of the proposed
method providing that the collocation points are sufficiently dense.
For numerical verification, direct solver and a subspace s...
In this paper, motivated by the Schulz method for finding the inverse of a nonsingular matrix, an inverse-free iterative algorithm for solving the discrete algebraic Riccati equation (DARE) is given in its transformation form. The convergence of the proposed algorithm is proved. Compared with some existing algorithms,...
Li Wang, Ying-Xiong Xiao, Xin-Rong Luo· Journal of Mathematical Stud...· 0 citations
Conjugate gradient methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems. In this paper, we suggest a new hybrid nonlinear conjugate gradient method, in which the conjugate gradient coefficient $\beta _{k}$ is a convex combination of $\beta _{k}^{NV...
A. Mehamdia, Y. Chaib, T. Bechouat· Uzbek Mathematical Journal· 0 citations
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