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Full-Text Articles in Theory and Algorithms
Three Contributions To The Theory And Practice Of Optimizing Compilers, Linxiao Wang
Three Contributions To The Theory And Practice Of Optimizing Compilers, Linxiao Wang
Electronic Thesis and Dissertation Repository
The theory and practice of optimizing compilers gather techniques that, from input computer programs, aim at generating code making the best use of modern computer hardware. On the theory side, this thesis contributes new results and algorithms in polyhedral geometry. On the practical side, this thesis contributes techniques for the tuning of parameters of programs targeting GPUs. We detailed these two fronts of our work below.
Consider a convex polyhedral set P given by a system of linear inequalities A*x <= b, where A is an integer matrix and b is an integer vector. We are interested in the integer hull PI of P which is the smallest convex polyhedral set that contains all the integer points in P. In Chapter …
The Design And Implementation Of A High-Performance Polynomial System Solver, Alexander Brandt
The Design And Implementation Of A High-Performance Polynomial System Solver, Alexander Brandt
Electronic Thesis and Dissertation Repository
This thesis examines the algorithmic and practical challenges of solving systems of polynomial equations. We discuss the design and implementation of triangular decomposition to solve polynomials systems exactly by means of symbolic computation.
Incremental triangular decomposition solves one equation from the input list of polynomials at a time. Each step may produce several different components (points, curves, surfaces, etc.) of the solution set. Independent components imply that the solving process may proceed on each component concurrently. This so-called component-level parallelism is a theoretical and practical challenge characterized by irregular parallelism. Parallelism is not an algorithmic property but rather a geometrical …