Title :
On Computing Solutions of Linear Diophantine Equations with One Non-linear Parameter
Author :
Grosslinger, Armin ; Schuster, Stefan
Author_Institution :
Dept. of Inf. & Math., Univ. of Passau, Passau, Germany
Abstract :
We present an algorithm for solving Diophantine equations which are linear in the variables, but non-linear in one parameter. We are looking for the pointwise solutions, i.e., the solutions for the unknowns in dependence of the value of the parameter. Solving Diophantine equations is central to computing the data dependences of certain codes (loops with certain array accesses) which often occur in scientific computing. Our algorithm enables the computation of data dependences in more general situations than is possible with current algorithms.
Keywords :
mathematics computing; array access; data dependence; linear Diophantine equation; nonlinear parameter; pointwise solution; scientific computing; Algorithm design and analysis; Concurrent computing; Data analysis; Informatics; Mathematics; Nonlinear equations; Runtime; Scientific computing; Structural engineering; Terminology; automatic loop parallelization; linear diophantine equations; non-linear parameter; polyhedron model; quasi-polynomials;
Conference_Titel :
Symbolic and Numeric Algorithms for Scientific Computing, 2008. SYNASC '08. 10th International Symposium on
Conference_Location :
Timisoara
Print_ISBN :
978-0-7695-3523-4
DOI :
10.1109/SYNASC.2008.33