@CONFERENCE\{IMM2006-05085,
    author       = "F. G. Gustavson and J. Wasniewski",
    title        = "Rectangular Full Packed Format  for {LAPACK} Algorithms Timings on Several Computers",
    year         = "2006",
    month        = "jun",
    keywords     = "Symmetric matrices, Factorization, Cholesky Algoritm, Inversion, Solution",
    edition      = "Springer",
    pages        = "10",
    booktitle    = "In Conference Proceedings of {PARA'}06 (is coming)",
    volume       = "",
    series       = "{LNCS} of Springer",
    editor       = "",
    publisher    = "Springer",
    organization = "",
    address      = "Para06, Umea, Sweden",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5085-full.html",
    abstract     = "We describe a new data format for storing
triangular and symmetric matrices called {RFP} (Rectangular Full
Packed). The standard two dimensional arrays of Fortran and C (also
known as full format) that are used to store triangular and symmetric
matrices waste nearly half the storage space but provide high performance via
the use of level\verb+~+3 {BLAS}. Standard packed format arrays fully utilize storage
(array space) but provide low performance as there are no level\verb+~+3
packed {BLAS}. We combine the good features of packed and full storage
using {RFP} format to obtain high performance using L3 (level\verb+~+3) {BLAS} as
{RFP} is full format. Also, {RFP} format requires exactly the same
minimal storage as packed format. Each full and/or packedsymmetric/triangular routine becomes a single new {RFP} routine. We
present {LAPACK} routines for Cholesky factorization, inverse and solution
computation in {RFP} format to illustrate this new work and to describe
its performance on the {IBM,} Itanium, {NEC,} and {SUN} platforms.
Performance of {RFP} versus {LAPACK} full routines for both serial and {SMP} 
parallel processing is about the same while
using half the storage. Performance is roughly one to a factor of 33 for
serial and one to a factor of 100 for {SMP} parallel
times faster than {LAPACK} packed routines. Existing {LAPACK} routines
and vendor
{LAPACK} routines were used in the serial and the {SMP} parallel study
respectively. In both studies Vendor L3 {BLAS} were used."
}