Matrix Inversion

Bazman · **Joined:** Mon, 29 Jan 2007 13:48:38 UTC **Posts:** 537

Hi there,

$(I + \frac{kA^{n+ \frac{1}{2}}}{2})U^{n+1} = (I - \frac{kA^{n+ \frac{1}{2}}}{2})U^n +kF^{n+ \frac{1}{2}}$

$U^{n+1} = (I + \frac{kA^{n+ \frac{1}{2}}}{2})^-1(I - \frac{kA^{n+ \frac{1}{2}}}{2})U^n +kF^{n+ \frac{1}{2}}$

Assuming F(t)=0

They then multiply out

$(I + \frac{kA^{n+ \frac{1}{2}}}{2})^{-1}(I - \frac{kA^{n+ \frac{1}{2}}}{2})U^n = I -kA +\frac{(kA)^2}{2} - \frac{(kA)^3}{4}$

where they have taken A=-A

But it seems to me they have more or less ignored the inverse in the multiplication above or is thre some reason why the inverse is equal to the original matrix?

S.O.S. Mathematics CyberBoard

Matrix Inversion

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