Newton methods for quasidifferentiable equations and their quadratic convergence

In this method we consider a truncation of the matrix series ∞i=0AiQBi,then prove its quadratic convergence and give three corresponding al gorithms.

The global convergence, strongconvergence, superlinear convergence and the rate of quadratic convergence are analyzed and proved.

Effect of calculation parameters on convergence speed of one-dimensional transient heat transfer series solution;

Study on convergence speed of high order P type iterative learning control algorithm;

Analysis of convergence speed of repetitive control system;

Improvement of convergence rates for the empirical Bayes test problem in scale exponential family;

Mean convergence rate of derivatives approximation by Lagrange interpolation operators;

Making use of the formula of and the inequality of,this paper has deduced two types of probabilistic approximation of C-semigroups and the estimating of convergent rate.

It has been shown that the convergent rate .

Then,using Taylor expansion of the semigroup,Holder s inequality and estimations of moment-generating functions of some suitable random variables,some briefly probabilistic approximations and estimations of convergent rates are obtained for C-semigroups.