GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
ScaLAPACK user's guide
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications
SIAM Journal on Scientific Computing
SVDPACKC (Version 1.0) User''s Guide
SVDPACKC (Version 1.0) User''s Guide
Cache efficient bidiagonalization using BLAS 2.5 operators
ACM Transactions on Mathematical Software (TOMS)
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
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This paper introduces block Householder reduction of a rectangular sparse matrix to small band upper triangular form. The computation accesses a sparse matrix only for sparse matrix dense matrix (SMDM) multiplications and for "just in time" extractions of row and column blocks. For a bandwidth of k + 1, the dense matrices are the k rows or columns of a block Householder transformation. Using an initial random block Householder transformation allows reliable computation of a collection of largest singular values. Block Householder reduction is numerically stable, is computationally efficient on multicore cache based computer architectures, and has good potential for scalable distributed memory parallelization.