Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
COMPUTATION OF GAUSSKRONROD QUADRATURE RULES WITH NONPOSITIVE WEIGHTS
 

Summary: COMPUTATION OF GAUSS­KRONROD QUADRATURE RULES
WITH NON­POSITIVE WEIGHTS
G. S. AMMAR \Lambda , D. CALVETTI y , AND L. REICHEL z
Abstract. Recently Laurie presented a fast algorithm for the computation of (2n + 1)­point
Gauss­Kronrod quadrature rules with real nodes and positive weights. We describe modifications of
this algorithm that allow the computation of Gauss­Kronrod quadrature rules with complex conjugate
nodes and weights or with real nodes and positive and negative weights.
Key words. orthogonal polynomials, indefinite measure, fast algorithm, inverse eigenvalue
problem
1. Introduction. Let dw be a nonnegative measure with support on the real
axis and an infinite number of points of increase. Assume that the moments ¯ k :=
R 1
\Gamma1 x k dw(x), k = 0; 1; 2; : : : , exist and are bounded. For notational convenience, we
assume that ¯ 0 = 1. An n­point Gauss quadrature rule for the integral
If :=
Z 1
\Gamma1
f(x)dw(x)
(1.1)
is a formula of the form

  

Source: Ammar, Greg - Department of Mathematical Sciences, Northern Illinois University

 

Collections: Mathematics