Triangular canonical forms for lattic rules of prime-power order
In this paper the authors develop a theory of t-cycle D-Z representations for s-dimensional lattice rules of prime-power order. Of particular interest are canonical forms which, by definition, have a D-matrix consisting of the nontrivial invariants. Among these is a family of triangular forms, which, besides being canonical, have the defining property that their Z-matrix is a column permuted version of a unit upper triangular matrix. Triangular forms may be obtained constructively using sequences of elementary transformations based on elementary matrix algebra. The authors main result is to define a unique canonical form for prime-power rules. This ultratriangular form is a triangular form, is easy to recognize, and may be derived in a straightforward manner. 12 refs.
- OSTI ID:
- 443503
- Journal Information:
- Mathematics of Computation, Vol. 65, Issue 213; Other Information: PBD: Jan 1996
- Country of Publication:
- United States
- Language:
- English
Similar Records
The canonical forms of a lattice rule
Representation of lattice quadrature rules as multiple sums