On the Shape of the Fixed Points of [f]([x]) = [A] [x] + [b]

  • G. Mayer
  • I. Warnke


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.


Unique Fixed Point Algebraic Solution Interval Vector Interval Matrix Point Matrice 
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© Springer-Verlag Wien 2001

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  • G. Mayer
  • I. Warnke

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