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5 High-Performance Optimization Programming     continued...

In general, one of the first steps in optimizing codes for these architectures is implementation of standard basic linear algebra subroutines (BLAS). These routines --- continuously being improved, expanded, and adapted optimally to more machines --- perform operations such as dot products and vector manipulations , as well as matrix/vector and matrix/matrix operations. Thus, operations, such as in equations (49), (53), or (57) and (58) can be executed very efficiently. In particular, if n is very large, segmentation among the processors may also be involved. A new library of FORTRAN 77 subroutines, LAPACK, focuses on design and implementation of standard numerical linear algebra tasks (e.g., systems of linear equations, eigenvalue and singular value problems) to achieve high efficiency and accuracy on vector processors, high-performance workstations, and shared-memory multiprocessors. At this writing, up-to-date information may be obtained by sending the message send index from LAPACK to the electronic mail address netlib@ornl.gov.