Gauss-Siedel method

Gauss-Siedel method is an iterative technique for the solution of sets of equations. Given, for example, a set of three linear equations... 

Equation (140) can be solved either using an iteration method such as the Gauss-Siedel method or a direct method such as tridiagonal-matrix algorithm (TDMA). Other methods, such as the Alternating-Direction Implicit (ADI) method combine iteration with the TDMA. 

The more sophisticated version of the above procedure is the Gauss-Siedel method. This method is based on the following iteration procedure ... 

Doing this speeds up the numerical calculation, which otherwise is slow because of the slow thermal response of the wall. From here the Gauss Siedel iteration method can be employed to solve the system of algebraic equations with a reasonable convergence criterion, for example. 

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