‎In this paper‎, ‎we use a complete pivoting strategy to compute the IUL preconditioner obtained as the by-product of the Backward Factored APproximate INVerse process‎. ‎This pivoting is based on the complete pivoting strategy of the Backward IJK version of Gaussian Elimination process‎. ‎There is a parameter $alpha$ to control the complete pivoting process‎. ‎We have studied the effect of dif...

In this paper, we have used a complete pivoting strategy to compute the left-looking version of RIF preconditioner. This pivoting is based on the complete pivoting strategy of the IJK version of Gaussian Elimination process. There is a parameter α to control the pivoting process. To study the effect of α on the quality of the left-looking version of RIF preconditioner with complete pivoting str...

Recently codes have been developed for computing the Cholesky factorization with complete pivoting of a symmetric positive semidefinite matrix for the serial LAPACK library. In the parallel ScaLAPACK library there are only routines for the unpivoted factorization in the positive definite case and no algorithms use complete pivoting. We aim to assess the feasibility of complete pivoting in ScaLA...

The growth factor plays an important role in the error analysis of Gaussian elimination. It is well known that when partial pivoting or complete pivoting is used the growth factor is usually small, but it can be large. The examples of large growth usually quoted involve contrived matrices that are unlikely to occur in practice. We present real and complex n n matrices arising from practical app...

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 th...

Gaussian elimination with partial pivoting (GEPP) has long been among the most widely used methods for computing the LU factorization of a given matrix. However, this method is also known to fail for matrices that induce large element growth during the factorization process. In this paper, we propose a new scheme, Gaussian elimination with randomized complete pivoting (GERCP) for the efficient ...

A new algorithm of Demmel et al. for computing the singular value decomposition (SVD) to high relative accuracy begins by computing a rank-revealing decomposition (RRD). Demmel et al. analyse the use of Gaussian elimination with complete pivoting (GECP) for computing the RRD. We investigate the use of QR factorization with complete pivoting (that is, column pivoting together with row sorting or...

We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is compl...