Is Gauss Quadrature Better than Clenshaw–Curtis?
نویسندگان
چکیده
منابع مشابه
Is Gauss Quadrature Better than Clenshaw-Curtis?
We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Seven-line MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O’Hara and Smith in the 1960s, the phenomenon is explained as ...
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Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornormalized eigenvectors of a symmetric tridiagonal matrix. An algorithm is also presented for c...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 2008
ISSN: 0036-1445,1095-7200
DOI: 10.1137/060659831