2,795 research outputs found
An iterative method for solving Fredholm integral equations of the first kind
The purpose of this paper is to give a convergence analysis of the iterative
scheme: \bee u_n^\dl=qu_{n-1}^\dl+(1-q)T_{a_n}^{-1}K^*f_\dl,\quad
u_0^\dl=0,\eee where with finite-dimensional approximations of
and for solving stably Fredholm integral equations of the first kind with
noisy data.Comment: 29 page
Hybrid functions approach to solve a class of Fredholm and Volterra integro-differential equations
In this paper, we use a numerical method that involves hybrid and block-pulse
functions to approximate solutions of systems of a class of Fredholm and
Volterra integro-differential equations. The key point is to derive a new
approximation for the derivatives of the solutions and then reduce the
integro-differential equation to a system of algebraic equations that can be
solved using classical methods. Some numerical examples are dedicated for
showing efficiency and validity of the method that we introduce
Dynamical Systems Method for solving ill-conditioned linear algebraic systems
A new method, the Dynamical Systems Method (DSM), justified recently, is
applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM
gives a new approach to solving a wide class of ill-posed problems. In this
paper a new iterative scheme for solving ICLAS is proposed. This iterative
scheme is based on the DSM solution. An a posteriori stopping rules for the
proposed method is justified. This paper also gives an a posteriori stopping
rule for a modified iterative scheme developed in A.G.Ramm, JMAA,330
(2007),1338-1346, and proves convergence of the solution obtained by the
iterative scheme.Comment: 26 page
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