Parallelization of the Symmetric Indefinite Factorization

Anastasia Kruchinina
University of Zagreb, Faculty of Science, Department of Mathematics
University of Zagreb, 2013



   author={Kruchinina, Anastasia},



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Parallel computing is a topic that became very popular in the last few decades. Parallel computers are being used in many different areas of science such as astrophysics, climate modelling, quantum chemistry, fluid dynamics and medicine. Parallel programming is a type of programming where computations can be performed concurrently on different processors or devices. There are two different approaches to parallel computing. One of them is moving the sequential program to multiple cores, which optimized for execution of the sequential code. The other one is the developing of programs for many-threads processors with a large number of light weight threads, such as graphics processing units (GPUs). There is a big difference in the design of many-threads GPUs and general-purpose CPUs. Depending on the problem we choose one of these architectures. The main purpose of this study is to develop an understanding of parallel programming on GPUs and implement an algorithm for symmetric indefinite factorization for CUDA-enabled GPUs. Symmetric indefinite matrices are matrices with both positive and negative eigenvalues. They are very important and they arise in many field of science. Some of those fields are nonlinear optimization problems that use Newton’s method, certain methods in nonlinear programming, the augmented system of general least squares problems, discretized incompressible Navier-Stokes equations, and control theory.
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