Iterative solution of simultaneous equations

Iterative solution of two matrix equations

We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations X + A∗X−1A = Q and X − A∗X−1A = Q, where Q is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton’s method and inversion free variants of the basic fixed point iteration are discussed in some detail for the...

On the Iterative Solution of Adjoint Equations

High order quadrature based iterative method for approximating the solution of nonlinear equations

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Iterative Solution of Nonlinear Equations of Hammerstein Type

Suppose X is a real Banach space and F,K : X → X are accretive maps. Under different continuity assumptions on F and K such that the inclusion 0 = u+KFu has a solution, iterative methods are constructed which converge strongly to such a solution. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X . Our method of proof is of independ...