Neumann series

If A is a square matrixMathworldPlanetmath, A<1, then I-A is nonsingular and (I-A)-1=I+A+A2+=k=0Ak. This is the Neumann series.
It provides approximations of (I-A)-1 when A has entries of small magnitude. For example, a first-order approximation is (I-A)-1I+A.
It is obvious that this is a generalizationPlanetmathPlanetmath of the geometric seriesMathworldPlanetmath.


Title Neumann series
Canonical name NeumannSeries
Date of creation 2013-03-22 15:25:49
Last modified on 2013-03-22 15:25:49
Owner georgiosl (7242)
Last modified by georgiosl (7242)
Numerical id 9
Author georgiosl (7242)
Entry type Theorem
Classification msc 15-00