 About 193 results  books.google.com 4.4 KronrodPatterson Quadrature KronrodPatterson quadrature formulae QKP,
knk[f] = nk ∑ ν=1 a[k]νf(x[k]ν), −1 ≤ x[k]ν ≤ 1 for the determination of I[f] = ∫ 1−1 f
(x)dx are defined as follows. Let QG n be the Gaussian quadrature formula with ... 

 books.google.com Such formulas are referred to as GaussKronrod quadrature formulas. Patterson
has extended it further by adding another In + 2 abscissas to the Kronrod rule
and arriving at a (4n + 3)point rule, which is exact for all polynomials of degree
less ... 

 books.google.com [1] Pierre Barrucand. Intégration numérique, abscisse de Kronrod–Patterson et
polynômes de Szeg ̋o. C. R. Acad. ... [12] Sotirios E. Notaris. Gauss–Kronrod
quadrature formulae for weight functions of Berstein–Szeg ̋o type. II. J. Comput. 

 books.google.com formula using these same points as well as n+l others: / n n+l w(x)f(x)dx = £c,/Gc,)
+2 djf(tj)+R2n+lf. ... Patterson generalized this by beginning with a 3point
Gaussian quadrature formula, adding 4 Kronrod points, and then continuing by
adding ... 

 books.google.com (x  £„+,„), in order for the quadrature formula Qn+m to be exact for all Pn+2mi €
Pn+2mi In other words, the ... Most importantly, Patterson [330] generalizes
Kronrod's idea of extending Gauss formulas by adding 2n + 2 abscissas to the ... 

 books.google.com FORTRAN (Formula Translator), 2, 26, 29, 30. ... GaussKronrod Patterson
quadrature, 292. ... Gaussian quadrature, See also specific methods, such as
GaussLaguerre, 260, 279291. admissible weight functions, 280, 282.
fundamental ... 

 books.google.com Since ∫ 1−1 Fn+2p−1 dx = ∫ 1−1 ̃Pn+pQp−1 dx + ∫ 1−1 Rn+p−1 dx, the
quadrature formula is exact for all polynomials ... Patterson's quadrature formulae
PATTERSON [1968] has applied the Kronrod's method successively, starting with
a 3 ... 

 books.google.com Since ∫ 1−1Fn+2p−1dx = ∫ 1−1 ̃Pn+pQp−1dx + ∫ 1−1Rn+p−1dx, the
quadrature formula is exact for all ... Patterson's quadrature formulae
PATTERSON [1968] has applied the Kronrod's method successively, starting with
a 3 point ... 

 books.google.com ... in the θ variable). Other types of nested rules (with an increasing number of
interlaced nodes) are possible (Kronrod, Patterson), but they are harder to
compute ... The quadrature formula is interpolatory. 2. The node polynomial qn (x
) = (x ... 

 books.google.com Kronrod formulas Formulas with m preassigned nodes, where « = 2m + 1 , have
been well studied. ... Although theoretical results go back to Stieltjes and later
Szego, the quadrature formulas themselves are named after Kronrod [28], who
computed ... A software package has been published by Patterson [40], but one
must be prepared to compute in much higher precision than that of the required
formula. 

 