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 Taylor polynomial. System of equations for the coefficients. Gottfried Ultimate Fellow Posts: 786 Threads: 121 Joined: Aug 2007 05/06/2015, 04:17 PM (This post was last modified: 05/06/2015, 06:49 PM by Gottfried.) (05/06/2015, 02:42 PM)marraco Wrote: (05/05/2015, 07:40 AM)Gottfried Wrote: P*A = A*Bb I think that we are speaking of different things. Obviously, there should be a way to demonstrate the equivalence of both, because they are trying to solve the same problem; looking for the same solution. But as I understand, the Carleman matrix A only contains powers of a_i coefficients, yet if you look at the red side, it cannot be written as a matrix product A*Bb, because it needs to have products of a_i coefficients (like $a_1^3.a_3^2.a_5^8.a_...$). Maybe it is a power of A.Bb, or something like A^Bb? No, no ... In your convolution-formula you have in the inner of the double sum powers of powerseries (the red-colored formula $a^{ \;^x a}$ in your first posting ) with the coefficients of the a()-function (not of its single coefficients), and if I decode this correctly, then this matches perfectly the composition of V(x)*A * Bb = (V(x)*A) * Bb = [1,a(x), a(x)^2, a(x)^3),...] * Bb = V(a(x))*Bb Only, that after removing of the left V(x)-vector we do things in different order: V(x)*A * Bb = V(x)*(A * Bb ) and I discuss that remaining matrix in the parenthese of the rhs. That V(x) can be removed on the rhs and on the lhs of the matrix-equation must be justified; if anywhere occur divergent series, this becomes difficult, but as far as we have nonzero intervals of convergence for all dot-products, this exploitation of associativity can be done /should be possible to be done (as far as I think). (The goal of this all is of course to improve computability of A, for instance by diagonalization of P or Bb and algebraic manipulations of the occuring matrix-factors). Anyway - I hope I didn't actually misread you (which is always possible given the lot of coefficients... ) Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread Taylor polynomial. System of equations for the coefficients. - by marraco - 04/30/2015, 03:24 AM RE: Taylor polinomial. System of equations for the coefficients. - by tommy1729 - 05/01/2015, 08:37 AM RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/01/2015, 09:42 AM RE: Taylor polinomial. System of equations for the coefficients. - by tommy1729 - 05/01/2015, 09:43 PM RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/03/2015, 04:46 AM RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/03/2015, 12:07 PM RE: Taylor polinomial. System of equations for the coefficients. - by Gottfried - 05/05/2015, 07:40 AM RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/06/2015, 02:42 PM RE: Taylor polinomial. System of equations for the coefficients. - by Gottfried - 05/06/2015, 04:17 PM RE: Taylor polynomial. System of equations for the coefficients. - by marraco - 05/07/2015, 09:45 AM RE: Taylor polynomial. System of equations for the coefficients. - by marraco - 01/14/2016, 12:47 AM

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