CHAPTER 5. Iterative methods for solving Systems of Linear Equations

In the following document you are going to find some criteria to make a serious analysis of a numerical method e.g. convergence, consistency and stability. Short and simple definitions for these criteria are:

Convergence: a numerical model is convergent when it reaches an stable value which is close to the real answer.

Consistency: it depends on the truncation error. Et: f(dx,dy,dz,dt,..), so when each delta approaches zero (0) then Et approaches zero too, making consistent the numerical model.

Stability: a model is stable if its answer doesn`t fluctuate (oscillate) with the time.

Besides the usual iterative methods, you can read the meaning of a diagonally dominant matrix which is necessary to apply any method.

Iterative 1
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Over here you have a presentation with a kind of summary about the iterative methods:

Iterative 2
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