The cubic spline interpolation function is For a natural spline we found the i ’s by solving a matrix equation Aa = z . The purpose of this exercise is to find what this equation is for a clamped...

The cubic spline interpolation function is

For a natural spline we found the


_i
’s by solving a matrix equation
Aa
=
z. The purpose of this exercise is to find what this equation is for a clamped spline. Recall that for a clamped spline it is required that
’ (
₁) =
’1 and
 (

_n+1) =
’
<sub>n

+1</sub>, where
’₁
and
’
<sub>n

+1</sub>
are given. Show
a
= (
₁,

₂, ··· ,


_n+1)
^T

,
z
= (6
₁+2’₁, 6
₂, ··· , 6

_n
, 6

_n+1−2’
<sub>n

+1</sub>)
^T

, and
A
is the
× tridiagonal matrix

Also, once
a
is determined, then

₀
=

₂
− 2’¹
and


_n+2
=


_n

+ 2’
<sub>n

+1</sub>.