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Gautschi. Algorithm 726, orthogonal polynomials and Gauss-type quadratures(T)(42s).djvu |
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Size 0.5Mb Date Dec 19, 2004 |
recursion coefficients a/, /3/ for the Jacobi weight wia'^\-) = w{a-^\-;0)...
In this example we illustrate a slight variation of the discretization procedure
D.9)-D.13), which ends up with a discrete inner product of the same type as
in D.13) (and thus implementable by the routine mcdis), but derived in a
somewhat different manner...
The driver test7 implements this, with
n = 40 and an error tolerance 50 X es in single precision, and 1000 X ed in
double precision...
When divisions are
involved (iopt = 4, 5, and 6), however, the algorithms rapidly become unsta-
unstable as the point z = x + iy s С moves away from the support interval of d k...
The subroutines indp and dindp in the
driver testlO implement this procedure in single (resp., double) precision...
E.6)
E.7)
The point to observe is that {pk(z; dX)} is a minimal solution of the basic
recurrence relation A.3) for the orthogonal polynomials {тгк(-; dX)} (cf...
Rather remarkably, the coefficients are recov-
recovered to essentially full accuracy, even when the input coefficients (produced
by chri and dchri) are very inaccurate! This is certainly a phenomenon that
deserves further study...
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