A cubically convergent Newton-type method under weak conditions
نویسندگان
چکیده
منابع مشابه
An Efficient Cubically Convergent Two-Point Newton Method
A numerical procedure fo r solving non-linear equations is presented which is a modification of the Two Point Newton Method developed by the author earlier. It is shown that the method presented here has a third order convergence. The modified procedure incorporates computation of the x value for an intermediate point using the original Two Point Newton Method. The derivative of the intermediat...
متن کاملOn Constructing a Cubically Convergent Numerical Method for Multiple Roots
We propose the numerical method defined by xn+1 = xn − λ f(xn − μh(xn)) f ′(xn) , n ∈ N, and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-prec...
متن کاملCubically Convergent Iterations for Invariant
We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of Rn and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global be...
متن کاملOn a Cubically Convergent Iterative Method for Matrix Sign
We propose an iterative method for finding matrix sign function. It is shown that the scheme has global behavior with cubical rate of convergence. Examples are included to show the applicability and efficiency of the proposed scheme and its reciprocal.
متن کاملA Globally Convergent LP-Newton Method
We develop a globally convergent algorithm based on the LP-Newton method, which has been recently proposed for solving constrained equations, possibly nonsmooth and possibly with nonisolated solutions. The new algorithm makes use of linesearch for the natural merit function and preserves the strong local convergence properties of the original LP-Newton scheme. We also present computational expe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2008
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.08.013