He is the author of several well known books, including " " Nodes and weights of quadrature formulas.
2.
As a practical matter, high-order numeric integration is rarely performed by simply evaluating a quadrature formula for very large N.
3.
In contrast, Gaussian quadrature rules are not naturally nested, and so one must employ Gauss Kronrod quadrature formulas or similar methods.
4.
If we allow the intervals between interpolation points to vary, we find another group of quadrature formulas, such as the Gaussian quadrature formulas.
5.
If we allow the intervals between interpolation points to vary, we find another group of quadrature formulas, such as the Gaussian quadrature formulas.
6.
During the years 1913 1918, Peano published several papers that dealt with the remainder term for various numerical quadrature formulas, and introduced the Peano kernel.
7.
As an application, he computed the areas under the curves y = x ^ n an early integral which is known as Cavalieri's quadrature formula.
8.
Since the degree of f ( x ) is less than 2n-1, the Gaussian quadrature formula involving the weights and nodes obtained from p _ { n } ( x ) applies.
9.
This represents the most sophisticated use of the method of exhaustion in ancient mathematics, and remained unsurpassed until the development of integral calculus in the 17th century, being succeeded by Cavalieri's quadrature formula.
10.
Gauss Kronrod formulas are extensions of the Gauss quadrature formulas generated by adding n + 1 points to an n-point rule in such a way that the resulting rule is of order 2n + 1 (; the corresponding Gauss rule is of order 2n-1 ).
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