Thread Rating:
• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Taylor polynomial. System of equations for the coefficients. marraco Fellow Posts: 100 Threads: 12 Joined: Apr 2011 05/06/2015, 02:42 PM (This post was last modified: 05/06/2015, 02:52 PM by marraco.) (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? The Pascal matrix on the blue side is the exponential of a much simpler matrix $ \exp \left ( \left [ \begin{matrix} . & 1 & . & . & . & . & . \\ . & . & 2 & . & . & . & . \\ . & . & . & 3 & . & . & . \\ . & . & . & . & 4 & . & . \\ . & . & . & . & . & 5 & . \\ . & . & . & . & . & . & 6 \\ . & . & . & . & . & . & . \end{matrix} \right ] \right ) = \left [ \begin{matrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ . & 1 & 2 & 3 & 4 & 5 & 6 \\ . & . & 1 & 3 & 6 & 10 & 15 \\ . & . & . & 1 & 4 & 10 & 20 \\ . & . & . & . & 1 & 5 & 15 \\ . & . & . & . & . & 1 & 6 \\ . & . & . & . & . & . & 1 \end{matrix} \right ]$ Maybe the equation can be greatly simplified by taking a logarithm of both sides. I have the result, but I do not yet know how to get it. « 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

 Possibly Related Threads... Thread Author Replies Views Last Post Arbitrary Order Transfer Equations JmsNxn 0 635 03/16/2021, 08:45 PM Last Post: JmsNxn New Quantum Algorithms (Carleman linearization) Finally Crack Nonlinear Equations Daniel 2 1,434 01/10/2021, 12:33 AM Last Post: marraco Moving between Abel's and Schroeder's Functional Equations Daniel 1 3,030 01/16/2020, 10:08 PM Last Post: sheldonison Taylor series of i[x] Xorter 12 23,065 02/20/2018, 09:55 PM Last Post: Xorter Taylor series of cheta Xorter 13 25,233 08/28/2016, 08:52 PM Last Post: sheldonison Totient equations tommy1729 0 3,324 05/08/2015, 11:20 PM Last Post: tommy1729 Bundle equations for bases > 2 tommy1729 0 3,387 04/18/2015, 12:24 PM Last Post: tommy1729 Grzegorczyk hierarchy vs Iterated differential equations? MphLee 0 3,551 01/03/2015, 11:02 PM Last Post: MphLee A system of functional equations for slog(x) ? tommy1729 3 8,124 07/28/2014, 09:16 PM Last Post: tommy1729 partial invariant equations ? tommy1729 0 3,243 03/16/2013, 12:32 AM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)