bo198214 Wrote:Gottfried Wrote:It means, we can have different eigenmatrices / sets of eigenvectors resulting in the same composition for the infinite matrix Bs.
Oh you mean for the infinite matrices! But the truncated matrices have a unique decomposition. And you use truncated matrices to approximate the solution. So how does this fit into your considerations?
... approximately... ;-) You may have different series, which asymptotically compute gamma(something), truncated give good approximations as well.
The terms of X*D*X^-1 are finite polynomials in t and tl, and - a guess for answering - they may be expressed differently by the different roots of these polynomials... Then they are also summed by weights of binomial-coefficients and finally weighted by powers of 1/t to produce the terms for Bs.
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A situation, where two different infinite series occur, is the case of
1/3 = lim 1/2 - 1/4 + 1/8 - 1/16 ... = 1/2 / (1 + 1/2)
1/3 = lim 1 -2 +4 - 8 +16 ... // analytic continuation for 1 / (1 + 2)
Possibly this analogy is better, since in the example we have an alternating convergent series for t=2 and an alternating divergent series for t=4 for the final construction of terms.
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Gottfried Helms, Kassel