# Trying to find an easy way to solve this

## Homework Statement n/a

## The Attempt at a Solution

I understand that I could make a REALLY complicated recurrence relation, one involving like 5 nested for loops, but I would prefer a better way of finding d1, ..., dn.

Is there a better way?

Uuh, what is the complete question?? All I can see is the question "Compute coefficients so that the polynomial..."

Maybe attach your pdf to here??

## Homework Statement n/a

## The Attempt at a Solution

I understand that I could make a REALLY complicated recurrence relation, one involving like 5 nested for loops, but I would prefer a better way of finding d1, ..., dn.

Is there a better way?

Whoops!

" ... so that the polynomial satisfies the n conditions

p(t1) = b1 , ... , p(tn) = bn "

Is the recurrence THAT complicated?? I'm really surprised how you can find 5 nested loops for this problem. Care to explain your reasoning?

What you could do is calculate (theoretically) p(t1),...,p(tn), and see what you get. It shouldn't be that hard...

Is the recurrence THAT complicated?? I'm really surprised how you can find 5 nested loops for this problem. Care to explain your reasoning?

What you could do is calculate (theoretically) p(t1),...,p(tn), and see what you get. It shouldn't be that hard...

I still think it's complicated.

We have

b1 = d1
b2 = d1 + d2(t2 - t1)
b3 = d1 + d2(t3 - t1) + d3(t3 - t1)(t3 - t2)
b4 = d1 + d2(t4 - t1) + d3(t4 - t1)(t4 - t2) + d4(t4 - t1)(t4 - t2)(t4 - t3)
.
.
.

And it got really messy when I tried to find a general formula for di in terms of di-1

Ah, yes, I see the problem

I still think it's complicated.

We have

b1 = d1
b2 = d1 + d2(t2 - t1)
b3 = d1 + d2(t3 - t1) + d3(t3 - t1)(t3 - t2)
b4 = d1 + d2(t4 - t1) + d3(t4 - t1)(t4 - t2) + d4(t4 - t1)(t4 - t2)(t4 - t3)
.
Express this as a system of linear equations, and thus as matrices. MATLAB is really good in solving these!

And it got really messy when I tried to find a general formula for di in terms of di-1

Don't worry with a general formula. I suppose you'll only need to solve it for specific values...

Ah, yes, I see the problem

.
Express this as a system of linear equations, and thus as matrices.

Ooooooooooohhhhhhh! HOW DID I NOT SEE THAT BEFORE?

[URL]http://www.gifbin.com/bin/1233445870_ae19b02.gif[/URL]

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Ah, yes, I see the problem

.
Express this as a system of linear equations, and thus as matrices. MATLAB is really good in solving these!

Don't worry with a general formula. I suppose you'll only need to solve it for specific values...

Is this the sort of set-up I'll have? Yes, it would be something like that that you'll get.