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Smoothing Newton method for operator equations in Banach spaces
In this paper, the global and superlinear convergence of smoothing Newton method for solving nonsmooth operator equations in Banach spaces are shown....
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A refined semilocal convergence analysis of an algorithm for solving the Ricatti equation
The semilocal convergence of a numerical algorithm for solving the algebraic Ricatti equation with multiparameter singularly perturbed systems is...
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An inverse-free Newton-Jarratt-type iterative method for solving equations under the gamma condition
A local as well as a semilocal convergence analysis for Newton–Jarratt–type iterative method for solving equations in a Banach space setting is...
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On a quadratically convergent method using divided differences of order one under the gamma condition
We re-examine a quadratically convergent method using divided differences of order one in order to approximate a locally unique solution of an...
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Visualizing parametric solution sets
We characterize the boundary ∂Σ p of the solution set Σ p of a parametric linear system A ( p ) x = b ( p ) where the elements of the n × n matrix and the...
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An improved unifying convergence analysis of Newton’s method in Riemannian manifolds
Using more precise majorizing sequences we provide a finer convergence analysis than before [1], [7] of Newton’s method in Riemannian manifolds with...
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On the Convergence of Broyden-Like Methods
The author provides a finer local as well as semilocal convergence analysis of a certain class of Broyden-like methods for solving equations...
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On the convergence of the secant method under the gamma condition
We provide sufficient convergence conditions for the Secant method of approximating a locally unique solution of an operator equation in a Banach...
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A refined theorem concerning the conditioning of semidefinite programs
Using a weaker version of the Newton-Kantorovich theorem [6] given by us in [3], we show how to refine the results given in [8] dealing with the...
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Robust Approximate Zeros in Banach Space
We extend Smale’s concept of approximate zeros of an analytic function on a Banach space to two computational models that account for errors in the...
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The prime-counting function and its analytic approximations
The paper describes a systematic computational study of the prime counting function π ( x ) and three of its analytic approximations: the logarithmic...
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Energy drift in molecular dynamics simulations
In molecular dynamics, Hamiltonian systems of differential equations are numerically integrated using the Störmer–Verlet method. One feature of these...
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On a nonsmooth version of Newton’s method using locally lipschitzian operators
In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in Banach space using Newton’s...
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Dirichlet Forms Methods: An Application to the Propagation of the Error Due to the Euler Scheme
We present recent advances on Dirichlet forms methods either to extend financial models beyond the usual stochastic calculus or to study stochastic...
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Geometry of interpolation sets in derivative free optimization
We consider derivative free methods based on sampling approaches for nonlinear optimization problems where derivatives of the objective function are...
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Relaxing the convergence conditions for Newton-like methods
Local as well as semilocal convergence theorems for Newton-like methods have been given by us and other authors [1]—[8] using various Lipschitz type...
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A convergence analysis and applications for two-point Newton-like methods in Banach space under relaxed conditions
We provide a local as well as a semilocal convergence analysis for two-point Newton- like methods in a Banach space setting under very relaxed...
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A Modification of the Sampling Series with a Gaussian Multiplier
We propose a modification of the sampling series using a Gaussian multiplier. Error estimates for the modified series to approximate a band-limited...
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New sufficient convergence conditions for the secant method
We provide new sufficient conditions for the convergence of the secant method to a locally unique solution of a nonlinear equation in a Banach space....
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Linear Systems Arising for Second-Order Mimetic Divergence and Gradient Discretizations
Recent investigations by Castillo and Grone have led to a new method for constructing mimetic discretizations of divergence and gradient operators....