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3. Iterative methods
In this chapter we again consider the problem of solving a linear equation of the form Ax = b, where A is an invertible matrix, but instead of looking for an algorithm to obtain the solution directly, if it exists, we examine iteration procedures that can create a convergent sequence of vectors (x n ), having the desired solution as its limit.
This type of method is widely used for large-scale problems, when the matrix A contains many zero coefficients outside its diagonal.
Please refer to chapter 10 of
3.1 Theoretical...
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Iterative methods
Euclidean methods
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Numerical calculation software and libraries
The actual implementation of the methods described above requires highly precise computer techniques which the size of this article does not allow us to cover. In any case, "off-the-shelf" programs are not always well-suited to real-life situations, which may require prior simplifications, estimates of tolerable errors, etc.
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