Numerisk - Spline

[JKDahl]

Hei!

Kan noen hjelpe meg litt med denne? Skjønner ikke helt hvordan jeg skal gå fram for å utlede den første formelen i oppgaven.

We shall study and construct splines of degree 2 on the knots
a = x[sub]0[/sub] < x[sub]1[/sub] < ... < x[sub]n[/sub] = b.
a) Consider the construction of the quadratic spline interpolating the data
x || x[sub]0[/sub] | ... | xn
f(x) || f[sub]0[/sub] | ... | fn

and with the extra condition s'(x[sub]0[/sub]) = 0. Derive the linear system of equations to be solved to compute the s'[sub]i[/sub], i = 0, ... ,n by means of the f[sub]i[/sub], i = 0, ... ,n. Here s'[sub]i[/sub] := s'(x[sub]i[/sub]).

Consider then the data
x || 0 | 5 | 1
f(x) || 1 | 2 | 0:5

Solve the linear system you obtained to construct the quadratic spline,
and give an expression for the spline as a polynomial of degree 2 on each
subinterval I[sub]0[/sub] and I[sub]1[/sub][sup]1[/sup].