 My Math Forum Need some insights for approximating curves
 User Name Remember Me? Password

 Linear Algebra Linear Algebra Math Forum

 July 23rd, 2018, 03:13 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 Need some insights for approximating curves Data Point: (-3, 1), (-1, 0), (0, 5), (2, 0), (4, 1) Using the following basis to approxmiate the above points.. The five basis: $\displaystyle 1, \sin(x \frac{\pi}{2}), \sin(x \frac{\pi}{4}), \cos(x \frac{\pi}{2}), \cos(x \frac{\pi}{6})$ $\displaystyle \begin{bmatrix} 1 & 1 & -\frac{1}{\sqrt{2}} & 0 & 0 \\ 1 & -1 & -\frac{1}{\sqrt{2}} & 0 & \frac{\sqrt{3}}{2} \\ 1 & 0 & 0 & 1 & 1 \\ 1 & 0 & 1 & -1 & 0.5 \\ 1 & 0 & 0 & 1 & -0.5 \end{bmatrix} \begin{bmatrix} t_4 \\ t_3 \\ t_2 \\ t_1 \\ t_0 \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ 5 \\ 0 \\ 1 \end{bmatrix}$ Would anyone please share any insights as to how the above big matrix was formed? Last edited by skipjack; July 24th, 2018 at 12:54 AM. July 23rd, 2018, 06:52 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,530 Thanks: 1390 let that matrix be $A$ let $b$ be a vector of the 5 basis functions as a function of $x$ let $d = (d_1,d_2)$ be the vector of ordered pairs $A_{i,j} = b_j(d_{i,1})$ Thanks from topsquark and zollen July 24th, 2018, 03:25 PM #3 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 How the basis were chosen? I sensed there were hidden rules for choosing these 5 basis. I did some experiments with the following basis of my choosing. $\displaystyle 1, \sin(x \frac{\pi}{2}), \cos(x \frac{\pi}{4}), \sin(x \frac{\pi}{6}), \cos(x \frac{\pi}{8})$ It did not yield the correct result of t0, t1, t2, t3 and t4. Last edited by skipjack; July 24th, 2018 at 05:35 PM. July 24th, 2018, 03:32 PM #4 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 I think it is based on Fourier series.... July 24th, 2018, 04:11 PM #5 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 Here is the formula: $\displaystyle y(x) = a_0 + a_1 \sin(x \frac{\pi}{2}) + a_2 \sin(x \frac{\pi}{4}) + a_k \sin(x \frac{\pi}{2k}) + b_1 \cos(x \frac{\pi}{2}) + b_2 \cos(x \frac{\pi}{4}) +\, ... + b_{k-1} \cos( x \frac{\pi}{2(k - 1)})$ Last edited by skipjack; July 24th, 2018 at 05:34 PM. July 25th, 2018, 05:14 AM #6 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 But.. what term should I pick for the matrix of nxn sizze?? July 25th, 2018, 03:57 PM   #7
Senior Member

Joined: Jan 2017
From: Toronto

Posts: 209
Thanks: 3

Quote:
 Originally Posted by zollen Here is the formula: $\displaystyle y(x) = a_0 + a_1 \sin(x \frac{\pi}{2}) + a_2 \sin(x \frac{\pi}{4}) + a_k \sin(x \frac{\pi}{2k}) + b_1 \cos(x \frac{\pi}{2}) + b_2 \cos(x \frac{\pi}{4}) +\, ... + b_{k-1} \cos( x \frac{\pi}{2(k - 1)})$
Would anyone able to tell me what formula is that? I thought it was fourier but it wasn't.... July 25th, 2018, 05:14 PM   #8
Senior Member

Joined: Sep 2015
From: USA

Posts: 2,530
Thanks: 1390

Quote:
 Originally Posted by zollen Would anyone able to tell me what formula is that? I thought it was fourier but it wasn't....
it looks like maybe it's a truncated combo of sine and cosine series but I suspect it's just some sinusoidal basis they threw together for this problem. Tags approximating, curves, insights Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Raxmo Probability and Statistics 6 December 28th, 2016 09:14 PM arithmetic Number Theory 0 October 9th, 2016 07:19 PM Pacopag Calculus 2 November 1st, 2011 04:35 AM mdoni Applied Math 0 February 18th, 2011 01:39 PM julian21 Number Theory 5 October 6th, 2010 07:55 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.      