Abstract
The use of matrix visualization in the design and development of numerical algorithms for supercomputers is discussed. Using color computer graphics, numerical analysts can gain new insights into algorithm behavior, which can then be used to design more efficient (parallel) numerical algorithms. The application of a matrix visualization tool, MatVu, in the design of algorithms from numerical linear algebra is the primary focus. Specific examples include the derivation of optimal preconditioning matrices for a conjugate gradient method, the design of parallel hybrid algorithms for solving the symmetric eigenvalue problem, the effects of operator splitting in the solution of incompressible Navier-Stokes equations, and the monitoring of Jacobian matrices associated with the application of Newton's method to a corresponding nonlinear system of equations.
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