A New Method for Solving Ill-conditioned Linear Systems
نویسنده
چکیده
An accurate numerical method is established for matrix inversion. It is shown theoretically that the scheme possesses the high order of convergence of seven. Subsequently, the method is taken into account for solving linear systems of equations. The accuracy of the contributed iterative method is clarified on solving numerical examples when the coefficient matrices are ill-conditioned. All of the computations are performed on a PC using several programs written in Mathematica 7.
منابع مشابه
1 2 Ja n 20 06 DSM for solving ill - conditioned linear algebraic systems ∗ †
A standard way to solve linear algebraic systems Au = f, (*) with ill-conditioned matrices A is to use variational regularization. This leads to solving the equation (A * A + aI)u = A * f δ , where a is a regularization parameter, and f δ are noisy data, ||f − f δ || ≤ δ. Numerically it requires to calculate products of matrices A * A and inversion of the matrix A * A + aI which is also ill-con...
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تاریخ انتشار 2013