Lazy BLAS-3 Reduction to Banded Upper Triangular
Gary Howell
15 September 2011, 10h30 - 15 September 2011, 12h00 Salle/Bat : 455/PCRI-N
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In a "Lazy" or "Just in Time" decomposition algorithm, updates are deferred until columns or rows (row blocks .. column blocks) are to be eliminated. A one-sided example is the GMRES algorithm (corresponding to orthogonal reduction to Hessenberg form). Here we consider reduction by Householder transformations to bidiagonal or to banded triangular form. Because the only accesses to original matrix are extraction of blocks and mutliplication by it, the lazy algorithm is easy to apply to sparse matrices. For a reduction to banded form, almost all the operations are BLAS-3. One use is determining a set of largest singular values of a sparse matrix.
