Filter löschen
Filter löschen

Help with finding and plotting interpolating polynomials

5 Ansichten (letzte 30 Tage)
Steven
Steven am 20 Apr. 2012
I already plot using lagrange and newton polynomial but I need help with finding and plotting the interpolating polynomials by system of equations. It doesn't say anywhere in my textbook on how to do this so I need help.
Here is the data I'm given for the problem:
Given the (fictitious) gasoline price data over 10 years,
Year, x 1986 1988 1990 1992 1994 1996
Price (¢),y 113.5 132.2 138.7 141.5 137.6 144.2
a simple interpolating polynomial is proposed as:
y(x)= c0 + c1x + c2x^2 + c3x^3 + c4 x^4 + c5 x^5
Then I am asked to find it by using:
a) System of equations
b) Lagrange polynomial
c) Newton polynomial
Please I need help for the system of equations part.
  1 Kommentar
Walter Roberson
Walter Roberson am 20 Apr. 2012
duplicate is at http://www.mathworks.com/matlabcentral/answers/35883-help-with-an-interpolation-problem

Melden Sie sich an, um zu kommentieren.

Antworten (1)

Richard Brown
Richard Brown am 20 Apr. 2012
I presume you mean c0 + c1x + c2x^2 + c3x^3 + c4 x^4 + c5 x^5
The system of equations method means treating c0 ... c5 as unknowns, plugging each data point into the equation, and forming a matrix (Vandermonde) equation to solve for the resulting linear equations in c0 ... c5. That should hopefully be enough to get you back underway
  4 Kommentare
Steven
Steven am 20 Apr. 2012
so what do the c's correspond to?
Walter Roberson
Walter Roberson am 20 Apr. 2012
Suppose you had x = 1, 2, 3, and y = 5, 8, 13. That would correspond to y = x^2 + 4, or y = 1 * x^2 + 0*x + 4, or c0 = 4, c1 = 0, c2 = 1. In order of descending coefficients, [1 0 4] . Now, does the 1 or the 4 correspond to one of the values [1 2 3] or [5 8 13]? No --the [1 0 4] are simply coefficients that make the polynomial work.
Extending this example with three values to the more generalized form,
y1 = c2*x1^2 + c1*x1 + c0
y2 = c2*x2^2 + c1*x2 + c0
y3 = c2*x3^2 + c1*x3 + c0
where x1, x2, x3 and y1, y2, y3 are known, then
let D = ((-x2+x1) * (-x3+x2) * (-x3+x1))
and then
c0 = ((x2*y3-x3*y2)*x1^2+(-x2^2*y3+x3^2*y2)*x1+x2*y1*x3*(-x3+x2)) / D
c1 = ((-y3+y2)*x1^2+(y3-y1)*x2^2+x3^2*(y1-y2)) / D
c2 = ((y3-y2)*x1+(-y3+y1)*x2-x3*(y1-y2)) / D
You can see that there is a _relationship_ between the x/y values and the c* coefficients, but you can also see that the c* are certainly not either the x or y values directly.

Melden Sie sich an, um zu kommentieren.

Kategorien

Mehr zu Polynomials finden Sie in Help Center und File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by