gaussian quadrature in a sentence

• Instead, spacing of latitudes is defined by the Gaussian quadrature.
• Gaussian quadrature often requires noticeably less work for superior accuracy.
• Gaussian quadrature is normally a good choice for smooth, non-singular problems.
• Special examples are the Gaussian quadrature for polynomials and the Discrete Fourier Transform for plane waves.
• Some suprisingly efficient methods, such as Gaussian quadrature, use evaluation at carefully chosen points.
• Note that Gaussian quadrature can also be adapted for various weight functions, but the technique is somewhat different.
• In Wikipedia article " Gaussian quadrature " the change of interval is presented as follows ( I quote ):
• In Gaussian quadrature, different weight functions lead to different orthogonal polynomials, and thus different roots where the integrand is evaluated.
• In contrast, Gaussian quadrature rules are not naturally nested, and so one must employ Gauss Kronrod quadrature formulas or similar methods.
• I think this is analogous to Chebyshev Quadrature but for arbitrary moments . ( This is like Gaussian quadrature but with equal weights.
• It's difficult to see gaussian quadrature in a sentence .
• Another approach is to use two Gaussian quadrature rules of different orders, and to estimate the error as the difference between the two results.
• If we allow the intervals between interpolation points to vary, we find another group of quadrature formulas, such as the Gaussian quadrature formulas.
• Here, the Gaussian quadrature is used, which states that one can always find weights w _ i and points x _ i such that
• In practice, several authors have observed that Clenshaw Curtis can have accuracy comparable to that of Gaussian quadrature for the same number of points.
• It may seem, therefore, that Clenshaw Curtis is intrinsically worse than Gaussian quadrature, but in reality this does not seem to be the case.
• Unlike Newton Cotes rules, which interpolate the integrand at evenly spaced points, Gaussian quadrature evaluates the function at the roots of a set of orthogonal polynomials.
• Barycentric or areal coordinates are extremely useful in engineering applications involving integrals often easier to evaluate, and Gaussian quadrature tables are often presented in terms of area coordinates.
• When the differential equation is more complicated, say by having an inhomogeneous diffusion coefficient, the integral defining the element stiffness matrix can be evaluated by Gaussian quadrature.
• If it is possible to change the points at which the integrand is evaluated, then other methods such as Gaussian quadrature and Clenshaw Curtis quadrature are probably more suitable.
• The zeros x _ j of the polynomials up to degree which are used as nodes for the Gaussian quadrature can be found by computing the eigenvalues of this tridiagonal matrix.