Abstract
Linear least squares problems arise in many important fields of science and engineering (such as econometry, geodesy, statistics, structural analysis, fluid dynamics, etc.). Applications from all these fields are to be handled numerically in the solution of various models used in the development of new industrial products. At the National Environmental Research Institute (Denmark), linear least squares problems have been applied in the efforts to determine optimal values of some of the parameters involved in air pollution models.
Large and sparse least squares problems can be handled by treating a sequence of dense blocks. Standard parallel subroutines, which perform orthogonal decomposition of dense matrices (as, for example, subroutines from LAPACK, SCALAPACK or NAG), can be used to handle successively the dense blocks. A preliminary reordering procedure, LORA, is to be applied at the beginning of the computational process. The size of the blocks can be adjusted to the particular computer used. Results obtained on a Silicon Graphics POWER CHALLENGE are given.
The same method can also be used in the solution of large and sparse systems of linear algebraic equations.
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Ostromsky, T., Salvini, S., Wasniewski, J., Zlatev, Z. (1996). Parallel solution of sparse problems by using a sequence of large dense blocks. In: Waśniewski, J., Dongarra, J., Madsen, K., Olesen, D. (eds) Applied Parallel Computing Industrial Computation and Optimization. PARA 1996. Lecture Notes in Computer Science, vol 1184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62095-8_60
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DOI: https://doi.org/10.1007/3-540-62095-8_60
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