polynomials with increasing order

hi, i want to create an equation of this format x^1+x^2+x^3........x^n. how can i do that?

Answer 1

[dpb]

doc polyval

NB: For higher orders numerics for polynomials get bad quickly. You can help somewhat by using the standardization technique documented in polyfit

[OLUBUKOLA ogunsola]

major problem is how to give the command such that matlab computes the x^1+ x^2 to x^n. thats important since i want to be able to input n as any number . if n was known i could write the x orders until i get to the highest, but i want it such that n could be anything

[Steven Lord]

n = 5;
x = zeros(1, n);

Now fill in x. But note that if you're using dpb's suggestion, the polynomial functions in MATLAB store coefficients in decreasing order not increasing. So this:

p = [1 2 3];

is 1*x^2 + 2*x + 3 not 1 + 2*x + 3*x^2.

result = polyval([1 2 3], 5)
y1 = 1*5^2 + 2*5 + 3
y2 = 1 + 2*5 + 3*5^2

[Image Analyst]

If x is a vector instead of a scalar, make sure you use dot caret instead of caret.

[dpb]

For the specific form outlined with all unity coefficients (and actually for any as Steven shows), Matlab already has the function--it's polyval. Ignoring the numerics issue on the hope you'll restrict [N,x] to reasonable values it's simply

N=4;
x=0.3;
y=polyval(ones(N,1),x);

It's simple enough to rewrite this just a little via a function handle so only the order and x is required

>> poly=@(n,x) polyval(ones(n,1),x);
>> n=3;
>> x=[0:0.1:0.4];
>> poly(n,x)
ans =
  1.0000    1.1100    1.2400    1.3900    1.5600
>>

NB: it's already vectorized as well.

You can deal with the issue of coefficients for the terms and even the order of the terms(*) if desired similarly.

(*) If you're adamant you want the order to be from constant to increasing power-of-x, then

poly=@(n,x) polyval(fliplr(ones(n,1)),x);

IOW, your function poly simply swaps the order in which it passes the coefficients to polyval--it's transparent to the use later. Of course, you have to be consistent and remember you can't pass the coefficient vector directly to the Matlab function.