 My Math Forum find a polynomial by interpolating 2 other polynomials
 User Name Remember Me? Password

 Real Analysis Real Analysis Math Forum

January 6th, 2015, 07:45 AM   #1
Newbie

Joined: Jan 2015
From: MOntreal

Posts: 1
Thanks: 0

find a polynomial by interpolating 2 other polynomials

Hi,

Have a look at the attached image. This is an aircraft performance chart. When we use these charts, we plot differents parameters (altitude, temperature, etc..) and, with a pencil, follow these curves and determine the value we are seeking for (fuel, time, distance, etc.)

I would like to acheive the same programmatically so I determined the polymnomials from the kown curves. However, there can be an infinite number of curves and when the plot falls between 2, I must find a way to come up with a new equation based on the interpolation of 2 polynomials.

The attached image shows a dotted line down to a reference line, then the user follow the closest curve (red) down to the know Y axis value, then vertically down (orange) to the value we are seeking.

What would you suggest?
Attached Images polynomial.jpg (20.3 KB, 2 views) January 21st, 2015, 06:03 AM #2 Senior Member   Joined: Aug 2008 From: Blacksburg VA USA Posts: 354 Thanks: 7 Math Focus: primes of course family of curves I have had some success with this type of interpolation IF the family of curves have a certain characterization ("nice") ( I think my subject was stochiometric curves of temp,press and a 3rd qty) For example, say you had 5 curves as a function of some parameter k, w/ asso quadratic fits (numbers are completely fabricated) AND they follow the same form with coefficients that track well with k. Say form is Y=Ax^2+Bx+C k=1 (A,B,C)= 5.42,3.11,4.2 k=2 (A,B,C)= 4.42,3.11,4.6 k=3 (A,B,C)= 3.42,3.11,5.0 k=4 (A,B,C)= 2.42,3.11,5.3 k=5 (A,B,C)= 1.42,3.11,5.7 From the above, one can then characterize "A" as a f{k}, as well as C. [ for example A= 6.42-k etc ] This allows you to direcly interpolate for 1< k<5 If you have infinite curves, I cannot help you ! Tags find, interpolating, polynomial, polynomials 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 taylor_1989_2012 Algebra 3 January 4th, 2013 06:55 AM miner Calculus 1 December 25th, 2011 11:02 AM wonger357 Algebra 1 April 30th, 2009 03:59 AM mine_cicek Linear Algebra 0 April 16th, 2009 03:12 PM xianghu21 Abstract Algebra 0 November 4th, 2008 07:22 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      