Displaying similar documents to “Increase of x n + 1 = x n - ϕ ( x n ) iteration's order.”

A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence

Kyurkchiev, Nikolay, Iliev, Anton (2009)

Serdica Journal of Computing

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This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv. In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence. ...

Three dimensional modelling of the peach in MAPLE

Bartoň, Stanislav

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Linearized Gauss-Newton iteration method is used to determine main axes of the three-dimensional ellipsoid approximating a peach. Three independent photos displaying the peach as ground, side, and front view are used as data sources. System MAPLE 11 was used as a computer environment. A practical example is presented in order to demonstrate the usage of all required commands. The quality of approximation is evaluated as a final part of the paper.

On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.

Laureano F. Escudero (1982)

Qüestiió

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We present an algorithm for supra-scale linearly constrained nonlinear programming (LNCP) based on the Limited-Storage Quasi-Newton's method. In large-scale programming solving the reduced Newton equation at each iteration can be expensive and may not be justified when far from a local solution; besides, the amount of storage required by the reduced Hessian matrix, and even the computing time for its Quasi-Newton approximation, may be prohibitive. An alternative based on the reduced...

Newton methods for solving two classes of nonsmooth equations

Yan Gao (2001)

Applications of Mathematics

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The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since...

An iterative procedure for solving the Riccati equation A₂R - RA₁ = A₃ + RA₄R

M. Thamban Nair (2001)

Studia Mathematica

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Let X₁ and X₂ be complex Banach spaces, and let A₁ ∈ BL(X₁), A₂ ∈ BL(X₂), A₃ ∈ BL(X₁,X₂) and A₄ ∈ BL(X₂,X₁). We propose an iterative procedure which is a modified form of Newton's iterations for obtaining approximations for the solution R ∈ BL(X₁,X₂) of the Riccati equation A₂R - RA₁ = A₃ + RA₄R, and show that the convergence of the method is quadratic. The advantage of the present procedure is that the conditions imposed on the operators A₁, A₂, A₃, A₄ are weaker than the corresponding...

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

Jonas Koko (2004)

International Journal of Applied Mathematics and Computer Science

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Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each...