## LDU decompositions with L and U well conditioned

J. M. Peña

### Abstract

We present, for some classes of matrices, $LDU$-decompositions whose unit triangular factors $L$ and $U$ are simultaneously very well conditioned. Our examples include diagonally dominant matrices by rows and columns and their inverses, Stieljes matrices and $M$-matrices diagonally dominant by rows or columns. We also show a construction of an accurate computation of the $LDU$-decomposition for any $M$-matrix diagonally dominant by rows or columns, which in turn can be applied to obtain an accurate singular value decomposition.

Full Text (PDF) [137 KB]

### Key words

conditioning, diagonal dominance, pivoting strategies, accuracy, singular value decomposition.

### AMS subject classifications

65F05, 65F35, 15A12.

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