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`.