QUADRATURE ERROR-BOUNDS WITH APPLICATIONS TO LATTICE RULES (VOL 33, PG 1995, 1996)

Reproducing kernel Hilbert spaces are used to derive error bounds and worst-case integrands for a large family of quadrature rules. In the c ase of lattice rules applied to periodic integrands these error bounds resemble those previously derived in the literature. However, the the ory developed here does not require periodicity and is not restricted to lattice rules. An analysis of variance (ANOVA) decomposition is emp loyed in defining the inner product. It is shown that imbedded rules a re superior when integrating functions with large high-order ANOVA eff ects.