Handling the conditioning of extreme-scale matrices – Massimiliano Fasi (Department of Mathematics, The University of Manchester)


Sala Seminari (Dip. Matematica).


In order to assess experimentally the stability of algorithms for the solution of systems of linear equations, it is typically desirable to have a certain degree of control over the condition number of the test matrices being used. If the tests are being performed at scale (e.g., in an HPL benchmark run for a TOP500 submission), it is necessary to ensure that generating the test data will take up only a negligible portion of the overall execution time required to solve the linear system. We develop two new techniques that satisfy these requirements and can be used to efficiently construct extremely large matrices with preassigned 2-norm condition number. Focusing on distributed memory environments, we discuss how these can be implemented in a communication-avoiding fashion.

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