In a previous task, I determined a polynomial interpolation using a system of linear equations.

Dachpunkt4cr

Dachpunkt4cr

Answered question

2022-02-23

In a previous task, I determined a polynomial interpolation using a system of linear equations.
The data points to be used were
((0,f(0)),(16,f(16)),(14,f(14)))
The linear equation used was of the form:
((02,01,00),(162,161,160),(142,141,140))
((a2),(a1),(a0))
((0),(13),(1))
and the polynomial of the form
p2(x)=a0+a1x+a2x2
was determined to have the coefficients
a0=0,a1=8+183,a2=48723
I am not aware of how I would use a system of linear equations to determine Q(x). Is it perhaps possible to derive the coefficients from p2? Or is there some other method of interpolation I should pursue?

Answer & Explanation

Ian Adams

Ian Adams

Skilled2022-03-07Added 163 answers

Instead of working with Q(x) Q(x)=b0+b1x+b2x12 wort with Φ(x) an Ψ(x) Φ(x)=(x12)Q(x)= =(b2b02)+x(b0b12)+b1x2=α+βx+γx2 Ψ(x)=(x12)F(x)=(x12)tan(πx) Ψ(x) is a very nice function for the range of interest. Compute α,β,γ and go back to b0,b1,b2.

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