more precision,a problem occured..
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Which command of matlab can I use so that my variables have more precision?? Because I want to apply the Jacobi method at the Hilbert matrix,but the determinant is zero,because of the limits number of digits...
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Roger Stafford
2013 年 11 月 30 日
Unless you use numbers in the Symbolic Toolbox or perhaps one of John D'Errico's File Exchange programs, there is no matlab command to use more than the 53-bit precision of matlab's double precision floating point numbers.
However, at the Wikipedia site
http://en.wikipedia.org/wiki/Hilbert_matrix
you will find an explicit formula for the elements of the inverse of the Hilbert matrix which might allow you to use ordinary 'double' numbers in applying the Jacobi method (as shown at:
http://en.wikipedia.org/wiki/Jacobi_method.)
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Roger Stafford
2013 年 12 月 1 日
To get negative values for your second input to 'nchoosek' would require an i or j out of the [1,250] range. How large did you allow them to get?
That however is not your main difficulty. The number n = 250 is way too large to be used with 'double' floating point. I advise you to use symbolic toolbox numbers which can be very large indeed. I won't undertake to tell you how to do that. You have to devote some time to reading your manuals to know how to make use of them. It requires some considerable study.
Walter Roberson
2013 年 12 月 1 日
Symbolic toolbox:
Each expression is
syms i j n
(-1).^(i+j) .* (i+j-1) .* nchoosek(n+i-1, n-j) .* nchoosek(n+j-1, n-i) .* nchoosek(i+j-2, i-1).^2
So I suspect you could then use
N = 250;
n = sym(N);
H_1 = sym(zeros(N,N));
for I = 1 : N
i = sym(i);
for J = 1 : N
j = sym(J);
H_1(I,J) = (-1).^(i+j) .* (i+j-1) .* nchoosek(n+i-1, n-j) .* nchoosek(n+j-1, n-i) .* nchoosek(i+j-2, i-1).^2;
end
end
If you ever wanted to convert it from symbolic numbers to decimal numbers, apply double() to it -- but expect round off and maybe overflow as well, if you do that.
4 件のコメント
Walter Roberson
2013 年 12 月 1 日
Note that the code you show her is for running inside MuPAD, not MATLAB directly. See evalin(symengine) and feval(symengine) for information on how you can invoke it from MATLAB.
It appears that you are somehow invoking the numeric nchoosek rather than the symbolic one. Please try some of the examples shown at http://www.mathworks.com/help/symbolic/nchoosek.html and see what happens
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