Question

Linear Algebra. please complete or show me how to to complete it. idk what to do. thank you

Curve Fitting It is desired to fit a polynomial curve through evenly spaced (x-direction) points. The general form of a polynomial is: f(x) = 4x + 4-1x* +ajx + ao If one wishes to fit a curve through, say 4 points, one would need a 3rd degree polynomial (n = 3) such that 4 unknown constants could be evaluated. In the absence of availability of many mathematical programming tools (Matlab, etc., Mathematica is available as an online program for student use), I would suggest that the polynomial coefficients can be determined with the appropriate simultaneous equations solved with a Linear Algebra technique. These coefficients can then be used in Excel to plot the fitted curve, along with the given points. Attached to this is one Excel graph for a similar data set to that requested for this project. (Simply using curve fitting provided by Excel is not acceptable.)

Answer 1

The Equation is ane {y - td {x3 y = arbat catch and the normal Equations ana bextc Ex Exy a{x+b{x²+cEx3 + dext Exy = a {x²+bExs+cExt+d Ext Exty = a&xt beah+c{x5+ d& no table The values Calculated using the following xy ay xy 19 au C 3 4 2 e x o V O 3 3 - 3 3 16 S 32 6 by 2 3 29 54 18 3 22 2 256 47 4 10 2 5 15 {a 4425 / 2osis Exs 9 243 728 6 1024 256 16 64 16 64 4096 3125 15625 50 250 625 125 25 142 552 15 55 225/99 Ex {x² Eno Exy Ext Ey Exy Exty Substiluting these values in normal Equations 15 6 at 15b+55(+225da 15 g + 555+226 +979 d = 41 By Applying Couss 55a + 225b+9196+4425d = 147 Elimination we go 58) 2254+9796+94256 +20515 e 1.2302 1,5251 -0.3532 0.0185 3 y(") - 1 - 2302 +1525x+0.3532 7 +0.0185 x 0 > 0 0 - JA) o 0 - 0

404 5- -15 -10 ол Б 10 15 ул --0+ о