Interpolation Formula in MATLAB | Solving for y(ti) with Code Example

[sara_87]

Homework Statement

If i have an interpolation formula, say:

$$y(t_i)=3+h\sum^i_{j=1}jy(t_j)$$

where i=0 to n
h=(a+b)/n
t_i=i*h
and
when i=0, we have: y(t₀)=0.

How would i write a code to find y(t_i)?

Homework Equations

The Attempt at a Solution

function y=examp(a,b,n)
h=(a+b)/n
for i=1:n+1
t(i)=(i-1)*h
for j=1:i+1

and now I am stuck because i don't know how write a code that uses the previous value of y to compute the next value of y.

 

[badphysicist]

Before the first loop, I would set up the y's(actually, it would be faster for your code to init the t's to zeros to, but unless n is very large it shouldn't matter):

y = zeros(n+1,1)

Then in the loop it would be something like
y(j) = 3 + sum( y(1:j-1).*(1:j-1) )

the .* does an element-wise product