The famous Newtonâ€“Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newtonâ€™s method to a solution of an equation. Here we present a â€œKantorovichâ€¦ (More)

Assuming that the first derivative of an operator satisfies the Lipschitz condition, a Kantorovich-type convergence criterion for inexact Newton methods is established, which includes the well-knownâ€¦ (More)

Protein expression in E. coli is the most commonly used system to produce protein for structural studies, because it is fast and inexpensive and can produce large quantity of proteins. However, whenâ€¦ (More)

We study the convergence properties for some inexact Newton-like methods including the inexact Newton methods for solving nonlinear operator equations on Banach spaces. A new type of residual controlâ€¦ (More)

An interesting problem was raised in Vong et al. (SIAM J. Matrix Anal. Appl. 32:412â€“429, 2011): whether the Ulm-like method and its convergence result can be extended to the cases of multiple andâ€¦ (More)

Convergence criterion of the inexact methods is established for operators with hÃ¶lder continuous first derivatives. An application to a special nonlinear Hammerstein integral equation of the secondâ€¦ (More)

We propose an Ulm-like Cayley transform method for solving inverse eigenvalue problems, which avoids solving approximate Jacobian equations comparing with other known methods. A convergence analysisâ€¦ (More)

and Applied Analysis 3 3. The Generalized Inexact Newton Method Let A : Rn â†’ S be continuously differentiable and let c = (c 1 , c 2 , . . . , c n ) T âˆˆ R. In what follows, we suppose that {Î» i (c)}â€¦ (More)