Abstract
Rook pivoting is a relatively new pivoting strategy used in Gaussian elimination (GE). It can be as computationally cheap as partial pivoting and as stable as complete pivoting. This paper shows some new attractive features of rook pivoting. We first derive error bounds for the LU factors computed by GE and show rook pivoting usually gives a highly accurate U factor. Then we show accuracy of the computed solution of a linear system by rook pivoting is essentially independent of row scaling of the coefficient matrix. Thus if the matrix is ill-conditioned due to bad row scaling a highly accurate solution can usually be obtained. Finally for a typical inversion method involving the LU factorization we show rook pivoting usually makes both left and right residuals for the computed inverse of a matrix small.
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Chang, XW. Some Features of Gaussian Elimination with Rook Pivoting. BIT Numerical Mathematics 42, 66–83 (2002). https://doi.org/10.1023/A:1021970102451
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DOI: https://doi.org/10.1023/A:1021970102451