ITERATIVE METHODS FOR SOLVING SYSTEMS OF LINEAR EQUATIONS

Iterative method

In computational mathematics, an iterative method attempts to solve a problem (for example, finding the root of an equation or system of equations) by finding successive approximations to the solution starting from an initial guess. This approach is in contrast to direct methods, which attempt to solve the problem by a finite sequence of operations, and, in the absence of rounding errors, would deliver an exact solution (like solving a linear system of equations Ax = b by Gaussian elimination). Iterative methods are usually the only choice for nonlinear equations. However, iterative methods are often useful even for linear problems involving a large number of variables (sometimes of the order of millions), where direct methods would be prohibitively expensive (and in some cases impossible) even with the best available computing power.

*GAUSS-SEIDEL

Gauss sediel

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*METHOD OF JACOBI

METHOD OF JACOBI

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REFERENCES:

(1)NUMERICAL METHODS FOR ENGINEERS WITH PERSONAL COMPUTER APPLICATIONS. STEVEN C. Chapra / Raymond P. CANALE

(2) internet-google.

(3)Enciclopedia libre wikipedia