Summary and Info
ABSTRACT: In every fi eld of scientifi с and industrial research, the extension of the use of computer science has resulted in an increasing need for computing power. It is thus vital to use these computing resources in parallel. In this thesis we seek to compute the canonical form of very large sparse matrices with integer coeffi cients, namely the integer Smith normal form. By 'Very large'', we mean a million indeterminates and a million equations, i.e. thousand billion of coeffi cients. Nowadays, such systems are usually not even storable. However, we are interested in systems for which many of these coeffi cients are identical; in this case we talk about sparse systems. We want to solve these systems in an exact way, i.e. we work with integers or in smaller algebraic structures where all the basic arithmetic operations are still valid, namely fi nitefi elds. The rebuilding of the whole solution from the smaller solutions is then relatively easy.
More About the Author
Jean Baptiste André Dumas (14 July 1800 – 10 April 1884) was a French chemist, best known for his works on organic analysis and synthesis, as well as the determination of atomic weights (relative atomic masses) and molecular weights by measuring vapor densities.
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