polyval error with recurrence relation

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T 2013-10-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/89295-polyval-error-with-recurrence-relation

评论： T 2013-10-11

function c = relation( n )
if n==0
   c = 1;
elseif n==1   
   syms x
   c = [x 0];
else
   syms x
   c = ((2*n-1)*x*[relation(n-1),0] - (n-1)*[0,0,relation(n-2)])/n;
   sum(c)
end
n=8
m=n+1;
xval=linspace(-1,1,5000)
I=trapsum(polyval(relation(n),xval).*polyval(relation(m),xval),-1,1);

Gives the following output:

??? Error using ==> polyval
Inputs to polyval must be floats, namely single or double.
Error in ==> polyval at 63
y = zeros(siz_x, superiorfloat(x,p));

What needs to be done to ensure that the output for the recurrence relation is a double?

I mean, in the function, we have syms x but this is to acquire the polynomial in analytic form. It's not necessary in this case but I need to plot it later on. The main issue I have is evaluating the integral using trapsum but I would need to do both; plot for various n, evaluate the integral.

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Walter Roberson 2013-10-6

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https://ww2.mathworks.cn/matlabcentral/answers/89295-polyval-error-with-recurrence-relation#answer_98782

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In your code for relation(), why do you have

sum(c)

which is just displaying the sum rather than returning the sum ?

After you build the relation symbolically, use

RelationM = relation(m);
RelationN = relation(n);
funM = matlabFunction(RelationM);
funN = matlabFunction(RelationN);
Y = funM(xval) .* funN(xval);
trapsum(Y, -1, 1)

However, I do not know what your trapsum routine does: it is not a routine in any Mathworks toolbox, and the obvious trapsum in the File Exchange uses a different calling sequence.

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T 2013-10-7

编辑：T 2013-10-7

在 MATLAB Online 中打开

    Adding c = sum(c); Gives the following:
function c = relation( n )
      if n==0
         c = 1;
      elseif n==1   
         syms x
         c = [x 0];
      else
         syms x
         c = ((2*n-1)*x*[relation(n-1),0] - (n-1)*[0,0,relation(n-2)])/n;
         c = sum(c)
      end
    n=3
    m=n+1;
    x =[-5:0.05:5];
  RelationM = relation(m);
  RelationN = relation(n);
  funM = matlabFunction(RelationM);
  funN = matlabFunction(RelationN);
    plot(x, funM(x))
??? Error using ==> mupadmex
Error in MuPAD command: Array sizes must match.
Error in ==> sym.minus at 14
    X = mupadmex('mllib::zip',A.s,B.s,'_subtract');
Error in ==> relation at 9
   c = ((2*n-1)*x*[relation(n-1),0] - (n-1)*[0,0,relation(n-2)])/n;
Error in ==> relation at 9
   c = ((2*n-1)*x*[relation(n-1),0] - (n-1)*[0,0,relation(n-2)])/n;
Error in ==> Q922 at 4
RelationM = relation(m);

Then I get the same message if I replace c = sum(c) with just sum(c) at:

??? Error using ==> times
Matrix dimensions must agree.
Error in ==> Q922 at 8
Y = funM(xval) .* funN(xval);

T 2013-10-8

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That's right. And for some reason using c1 and c2 will not generate the same polynomials for n where if you used

c = ((2*n-1)*x*[relation(n-1),0] - (n-1)*[0,0,relation(n-2)])/n;

The point was to do this using recursive programming.

T 2013-10-11

编辑：T 2013-10-11

在 MATLAB Online 中打开

Actually I don't think I need to do any of the above:

for n=0:inf
m=n+1;
int( ((2*n-1)*x*[relation(n-1),0] - (n-1)*[0,0,relation(n-2)])/n )* ((2*m-1)*x*[relation(m-1),0] - (m-1)*[0,0,relation(m-2)])/m),x,-1,1)
end

This will just give me zero. But is it possible to determine the round-off error? Or at least get the maximum value of n before the loop crashes?

I can set the recursion limit using:

set(0, 'RecursionLimit', 100000) but it keeps crashing still.

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