## Vectorization of multiple small matrix problems |

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Aiping Liao anrm any(anrm architectures automatic vectorizing compilers call m_backsolve(U call m_norm(A CMSSL computer vision converge Cornell Theory Center CRAY dimension A(p,n,n displays the speedup Distribute the problem-index Distributed Memory elementary linear algebra end do end FORTRAN global variables Householder QR IBM Corporation lems linear algebra algorithms loop the innermost loop transformations loops loop interchange matrices become tensors Matrix Problems Nikos multiple instance solver Multiple Small Matrix multiple small problem multiple-instance code multiple-instance problem n_prob not_done number of instances Optimal Control performance gain precompiler prob problem steps loop problem-index loop Problems Nikos Pitsianis Programming Languages QR decomposition RISC scalars become vectors Shirish Chinchalkar single-instance code Small Matrix Problems solves a single-instance Speedup versus Instance steps loop splitting stochastic differential equations subroutine m_backsolve(A supercomputers symmetric eigenvalue problem triangular backsolver Trust Region Vavasis and Yinyu vector hardware vector operations vector units vectors become matrices Visualizing second-order tensor