• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Kouznetsov-Tommy-Cauchy method tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 02/18/2015, 07:05 PM (This post was last modified: 02/18/2015, 10:48 PM by tommy1729.) Similar to the kouznetsov method I also consider a contour integral. But instead of taking THE shape of the contour and searching for the values on them , i give the values and search THE shape. Im close to proving this I think. This also implies that Im more optimistic about the traditional kouznetsov-cauchy method. I call it KTC-method which stands for Kouznetsov-Tommy-Cauchy method. Basicly the contour is split in 4 parts where the upper and lower are straight horizontal lines just like in Kouznetsov's method. The given values and the searched shape is thus in the almost vertical contourparts. Just like in Kouznetsov's method the precision is increased by " stretching " the contour to imaginary infinity. The values satisfy f(z*) = f*(z) , where * stands for complex conjugate , this to assure that we find a locally real-analytic solution. The main reason to support this and the Original Kouznetsov method is that the contour and its values only need to be continuous to imply that the interior is analytic. Then secondly by the functional equation and analytic continuation we get an analytic strip in both the upper and lower halfplane where we have an analytic sexp. These strips start at Im > 0 resp Im < 0 and are at least as high/low as Im(uppercurve ( the straith hor. line of the contour ) ) resp Im(lowercurve). Values should be chosen such that the path of the contour follow asymptotically f(a +/- bi) where b >> a. ( SO that we get close the fixpoint and get higher precision ) Preliminary results are optimistic. Pseudoperiod appears to become visible. Im not sure how do an update procedure to improve initial guesses and the alike , but even without that it seems to work. Excited regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Tommy's Gaussian method. tommy1729 24 3,959 11/11/2021, 12:58 AM Last Post: JmsNxn The Generalized Gaussian Method (GGM) tommy1729 2 392 10/28/2021, 12:07 PM Last Post: tommy1729 Arguments for the beta method not being Kneser's method JmsNxn 54 6,610 10/23/2021, 03:13 AM Last Post: sheldonison tommy's singularity theorem and connection to kneser and gaussian method tommy1729 2 497 09/20/2021, 04:29 AM Last Post: JmsNxn " tommy quaternion " tommy1729 14 5,323 09/16/2021, 11:34 PM Last Post: tommy1729 Why the beta-method is non-zero in the upper half plane JmsNxn 0 343 09/01/2021, 01:57 AM Last Post: JmsNxn Improved infinite composition method tommy1729 5 1,282 07/10/2021, 04:07 AM Last Post: JmsNxn A different approach to the base-change method JmsNxn 0 730 03/17/2021, 11:15 PM Last Post: JmsNxn A support for Andy's (P.Walker's) slog-matrix-method Gottfried 4 4,808 03/08/2021, 07:13 PM Last Post: JmsNxn Doubts on the domains of Nixon's method. MphLee 1 1,016 03/02/2021, 10:43 PM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)