Abstract
When solving linear systems of equations Cx = b (1) with a real n x n matrix C = (c ij ) and a real vector b with n components one often uses iterative methods - particularly when C is a large sparse matrix. Probably the most elementary iterative method can be derived from the socalled Richardson splitting C = I - A of C, where I is the identity matrix and A := I - C. This splitting induces the equivalent fixed point formulation x = Ax + b of (1) which leads to the iterative method x k+1 = Ax k + b.
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Mayer, G., Warnke, I. (2001). On the Shape of the Fixed Points of [f]([x]) = [A] [x] + [b]. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6280-4_15
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DOI: https://doi.org/10.1007/978-3-7091-6280-4_15
Publisher Name: Springer, Vienna
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