Question on a math equation

[blaxis10]

hello everyone,

While I was searching the net for my math problem, I found this site. If anyone can help me it is very appriciated. Also I have searched through this site but found nothing. I am taking numerical anaylsis lecture and I have a homework. and I am in trouble in some parts.

I got a general formula. it depends on the given x and y variables.
I am writing an example question so everybody can understand.

ex1; use langrange interpolation polynomial that approximate f(x)=x^3
a-)find the linear interpolation polynominal p1(x) using x0=1 and x1=2
b-)quadratic p2(x) x0=0, x1=1, x2=2

answer:
a-) langrange formula for p1there are 2 points given)
p1(x)=(y0*((x-x1)/(x0-x1)))+(y1*((x-x0)/(x1-x0)))

so if x0=1 y0=1^3=1(put x0 into f(x), so we find y0) and after that we have;
x0=1,y0=1
x1=2,y1=8
so when we replace the x and y varaibles into langrange;
p1(x)=(1*((x-2)/(1-2)))+(8*((x-1)/(2-1)))=(2-x)+8x-8=7x-6

p1(x)=7x-6 , SO this is answer. I found an approximation formula.

b-)langrange formula for p2there are 3 points given)
p2(x)=(y0*(((x-x1)*(x-x2))/((x0-x1)*(x0-x2))))+(y1*(((x-x0)*(x-x2))/((x1-x0)*(x1-x2))))+(y2*(((x-x0)*(x-x1))/((x2-x0)*(x2-x1))))

so if x0=0 y0=0^3=0 (put x0 into f(x), so we find y0) and after that we have;
x0=0,y0=0
x1=1,y1=1
x2=2,y2=8
so when we replace the x and y varaibles into langrange;
p2(x)=(0*(((x-1)*(x-2))/((0-1)*(0-2))))+(1*(((x-0)*(x-2))/((1-0)*(1-2))))+(8*(((x-0)*(x-1))/((2-0)*(2-1))))
p2(x)=(((x^2)-2x)/-1)+(((8x^2)-8x)/2)=2x-(x^2)+(4x^2)-8x=2x-(x^2)+(4x^2)-4x=(3x^2)-2x

p2(x)=(3x^2)-2x , SO this is answer. I found an approximation formula.

how can I calculate something like that in excel? and think that if we have 5 or 6 x variables how can we calculate also?

the general langrange formula is:


if anyone can solve this (developing a macro I think is the only way but I dont know anything about macros) It will very useful for me.

I got;
x0=-2, y0=-9,2
x1=-1, y1=-2,7
x2=0, y2=-1,5
x3=1, y3=0,4
x4=2, y4=7,2
x5=3, y5=26,1

thanks for every help.

 

[blaxis10]

Nobody knows how to solve?
please at least tell me how can I do a calculation like that?
(2x^2+3)*(3X^3+5x-2)=?
Please tell me a way to solve it.
thanks

 

[Oaktree]

Seems to me that you'd be much better off using a program like Matlab or Maple for this. Both of those are likely available at your university's computer lab, and simple Google queries (if not your textbook itself) should be able to provide specific instructions for how to use Matlab or Maple to perform the interpolation.

 

[blaxis10]

thanks for your answer. I will try the MATLAB. but do you know can I do a calculation like (2x^2+3)*(3X^3+5x-2)=? in excel? and if so, how can I find related documents? I dont know how to search it through google. thanks again for your answer.

 

[Oaktree]

do you know can I do a calculation like (2x^2+3)*(3X^3+5x-2)=? in excel?

What do you mean "do a calculation like..."? Excel can't do symbolic manipulation. You'd have to assign a value to X (presumably in a cell) and have your formula calculate =(2*(A1^2)+3)*(3*(A1^3)+5*A1-2) or similar