Computing symmetric rank-revealing decompositions via triangular factorization

Per Christian Hansen ( and P.Y. Yalamov

For a copy of this paper, either Abstract:

We present a family of algorithms for computing symmetric rank-revealing VSV decompositions, based on triangular factorization of the matrix. The VSV decomposition consists of a middle symmetric matrix that reveals the numerical rank in having three blocks with small norm, plus an orthogonal matrix whose columns span approximations to the numerical range and null space. We show that for semi-definite matrices the VSV decomposition should be computed via the ULV decomposition, while for indefinite matrices it must be computed via a URV-like decomposition that involves hyperbolic rotations.

rank-revealing decompositions, matrix approximation, symmetric matrices

AMS: 65F30, 65F35

IMM technical report 04/2000

Last update 21-3-2000 by fkc
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