Integrated Form of Continuous Newton’s Method
نویسندگان
چکیده
An integrated form of continuous Newton’s method is defined. Under rather minimal conditions the method is shown to lead to a zero of the given function. The result is applied to recover a recent Nash-Moser type inverse function theorem.
منابع مشابه
A Nash-moser Theorem with Near-minimal Hypothesis
A proof of a Nash-Moser type inverse function theorem is given under substantially weaker hypothesis than previously known. Our method is associated with continuous Newton’s method rather than the more conventional Newton’s method.
متن کاملConvergence of Newton's Method over Commutative Semirings
We give a lower bound on the speed at which Newton’s method (as defined in [5, 6]) converges over arbitrary ω-continuous commutative semirings. From this result, we deduce that Newton’s method converges within a finite number of iterations over any semiring which is “collapsed at some k ∈ N” (i.e. k = k + 1 holds) in the sense of [1]. We apply these results to (1) obtain a generalization of Par...
متن کاملConvergence Ball Analysis of a Modified Newton’s Method Under Hölder Continuous Condition in Banach Space
A modified Newton’s method which computes derivatives every other step is used to solve a nonlinear operator equation. An estimate of the radius of its convergence ball is obtained under Hölder continuous Fréchet derivatives in Banach space. An error analysis is given which matches its convergence order. 2010 Mathematics Subject Classification: 65B05, 47817, 49D15
متن کاملA continuous Newton-type method for unconstrained optimization
In this paper, we propose a continuous Newton-type method in the form of an ordinary differential equation by combining the negative gradient and Newton’s direction. It is shown that for a general function f(x), our method converges globally to a connected subset of the stationary points of f(x) under some mild conditions; and converges globally to a single stationary point for a real analytic ...
متن کاملAn Extension of Newton’s Method to ω-Continuous Semirings
Fixed point equations x = F (x) over ω-continuous semirings are a natural mathematical foundation of interprocedural program analysis. Equations over the semiring of the real numbers can be solved numerically using Newton’s method. We generalize the method to any ω-continuous semiring and show that it converges faster to the least fixed point than the Kleene sequence 0, F (0), F (F (0)), . . . ...
متن کامل