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On the local convergence of a family of Euler-Halley type iterations with a parameter
This paper aims to study the local convergence of a family of Euler-Halley type methods with a parameter α for solving nonlinear operator equations...
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An analysis of 4D variational data assimilation and its application
In this paper, we give an analysis and a general procedure for 4D variational data assimilation (4D-Var). In functional partial differential equation...
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A Semi-smooth Newton Method for Regularized State-constrained Optimal Control of the Navier-Stokes Equations
In this paper, we study semi-smooth Newton methods for the numerical solution of regularized pointwise state-constrained optimal control problems...
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Computing Stability of Differential Equations with Bounded Distributed Delays
This paper deals with the stability analysis of scalar delay integro-differential equations (DIDEs). We propose a numerical scheme for computing the...
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Numerical Computation of Connecting Orbits in Delay Differential Equations
We discuss the numerical computation of homoclinic and heteroclinic orbits in delay differential equations. Such connecting orbits are approximated...
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Newton iteration for partial differential equations and the approximation of the identity
It is known that the critical condition which guarantees quadratic convergence of approximate Newton methods is an approximation of the identity...
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Nonlinear multiscale decompositions: The approach of A. Harten
Data‐dependent interpolatory techniques can be used in the reconstruction step of a multiresolution scheme designed “à la Harten”. In this paper we...
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Denoising with higher order derivatives of bounded variation and an application to parameter estimation
Regularization with functions of bounded variation has been proven to be effective for denoising signals and images. This nonlinear regularization...
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On the rate of convergence of 2-term recursions in ℝ d
Let G be a compact set in ℝ d d ≥1, M = G × G and ϕ : M → G a map in C 3 ( M ). Suppose that ϕ has a fixed point ξ , i.e. ϕ ( ξ, ξ )= ξ . We investigate the rate of...
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Successive continuation for locating connecting orbits
A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs is considered. A local convergence...
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The convex-decomposable operator equation and its monotonic inclusive iteration
In this paper we discuss a class of nonlinear operators, that we name convex-decomposable operators, which have the nature: Fy−Fx≤(D 1 (x, y)+D 2 (x,...
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On a numerical Liapunov-Schmidt method for operator equations
Let, for a higher singular point x 0 of an operator equation G(x 0 )=0 and the kernels of the respective derivatives G ′( x 0 ) and G ′( x 0 ) * , see [1],...
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A projection method for computing turning points of nonlinear equations
A direct method for determining simple turning points of nonlinear parameterdependent equations is presented. Applications are discussed and...
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A comparison of point and ball iterations in the contractive map** case
In applications, one of the basic problems is to solve the fixed point equation x=Tx with T a contractive map**. Two theorems which can be...
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Path following around corank-2 bifurcation pints of a semi-linear elliptic problem with symmetry
Bifurcating solution branches and their numerical approximations of a semi-linear elliptic problem are considered at corank-2 bifurcaton points....
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Recurrence relations for rational cubic methods II: The Chebyshev method
We continue the analysis of rational cubic methods, initiated in [7]. In this paper, we obtain a system of a priori error bounds for the Chebyshev...
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A mesh-independence principle for nonlinear operator equations and their discretizations under mild differentiability conditions
In this note we extend the validity of the mesh-independence principle for nonlinear operator equations and their discretizations to include...
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Recurrence relations for rational cubic methods I: The Halley method
In this paper we present a system of a priori error bounds for the Halley method in Banach spaces. Our theorem supplies sufficient conditions on the...
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Splitting iteration method for simple singular points and simple bifurcation points
A splitting iteration method is introduced to compute the simple singular points and the simple bifurcation points of nonlinear problems. It needs...
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A continuation procedure based on projected Newton steps
In this paper we present and discuss a continuation method for solving certain fixed point problems in Hilbert spaces. The procedure allows to reduce...