On solving large and sparse systems of linear equations with multiple right-hand sides

  • Author: Benjamin Junge
  • Type: Bachelor's Thesis
  • Date: 2023-09-19
  • Reviewers: Prof. Dr. Michael Kuhn, Dr. Jens Saak


Solving large linear systems of equations involves an enormous consumption of resources, especially time and memory. These problems get amplified when considering systems with multiple right-hand sides. This thesis investigates the advantages of solving multiple right-hand sides at once and tests it with appropriate hardware and data. Two solving methods were implemented in two variants each: the inner loop variant and the outer loop variant. These variants were tested in an undisturbed computing environment and compared in terms of runtime and hardware events. The test results showed that the occurrence of the benefits depends on the selected tools. The available tools, Octave and OpenBLAS, were not suitable for demonstrating the benefits. However, a sample test showed that these benefits were present in Matlab. The results indicate that Octave is not well suited to take advantage of solving multiple right-hand sides at once. This was confirmed by extensive testing. On the other hand, the example test indicates that Matlab is better suited.

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