Orthogonal Rational Functions and Rational Gauss-type Quadrature Rules

Analysis Seminar
Wednesday, April 6, 2011 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
Consider a positive bounded Borel measure \mu with infinite supporton an interval [a,b], where -oo <= a < b <= +oo, and assume we have m distinctnodes fixed in advance anywhere on [a,b]. We then study the existence andconstruction of n-th rational Gauss-type quadrature formulas (0 <= m <= 2)that approximate int_{[a,b]} f d\mu. These are quadrature formulas with npositive weights and n distinct nodes in [a,b], so that the quadratureformula is exact in a (2n - m)-dimensional space of rational functions witharbitrary complex poles fixed in advance outside [a,b].