The canonical forms of a lattice rule

Conference · Thu Dec 31 00:00:00 EST 1992

OSTI ID:10120838

Lyness, J N

Much of the elementary theory of lattice rules may, be presented as an elegant application of classical results. These include Kronecker group representation theorem and the Hermite and Smith normal forms of integer matrices. The theory of the canonical form is a case in point. In this paper, some of this theory is treated in a constructive rather than abstract manner. A step-by-step approach that parallels the group theory is described, leading to an algorithm to obtain a canonical form of a rule of prime power order. The number of possible distinct canonical forms is derived, and this is used to determine the number of integration lattices having specified invariants.

• Research Organization: Argonne National Lab., IL (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 10120838
• Report Number(s): ANL/MCS/CP-78196; CONF-9211161-1; ON: DE93005686
• Resource Relation: Conference: 4. numerical integration conference,Oberwolfach (Germany),8-14 Nov 1992; Other Information: PBD: [1992]
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MATRICES
CANONICAL TRANSFORMATIONS
ALGORITHMS
ITERATIVE METHODS
GROUP THEORY
NUMERICAL SOLUTION
990200
MATHEMATICS AND COMPUTERS