This dissertation focuses on a widely used linear algebra kernel to solve linear systems, that is the LU decomposition. Usually, to perform such a computation one uses the Gaussian elimination with partial pivoting (GEPP). The backward stability of GEPP depends on a quantity which is referred to as the growth factor, it is known that in general GEPP leads to modest element growth in practice. H...

In this paper, we propose a novel method for subspace estimation used high resolution method without eigendecomposition where the sample Cross-Spectral Matrix (CSM) is replaced by upper triangular matrix obtained from LU factorization. This novel method decreases the computational complexity. The method relies on a recently published result on Rank-Revealing LU (RRLU) factorization. Simulation ...

Semi-symmetric three-way arrays are essential tools in blind source separation (BSS) particularly in independent component analysis (ICA). These arrays can be built by resorting to higher order statistics of the data. The canonical polyadic (CP) decomposition of such semi-symmetric three-way arrays allows us to identify the so-called mixing matrix, which contains the information about the inten...

Abstract-A new parallel algorithm for the LU factorization of a given dense matrix A is described. The case of banded matrices is also considered. This algorithm can be combined with Sameh and Brent’s [SIAM J. Numer. Anal. 14, 1101-I 113. (1977)] to obtain the solution of a linear system of algebraic equations. The arithmetic complexity for the dense case is in’ ($bn in the banded case), using ...

In this paper, we analyze the runtime performance of the LU factorization algorithm. To do this, we first test the basic algorithm, as well as a blocked algorithm across different compiler flags. Then, we add other specific optimizations to the blocked algorithm code in order to get the best runtime performance possible.

The Gauss–Borel or LU factorization of Gram matrices bilinear forms is the pivotal element in discussion theory biorthogonal polynomials. construction families polynomials and its second kind functions, spectral modeling multiplication by independent variable x, Christoffel–Darboux kernel projection properties, are discussed from this point view. Then, Hankel case presented different specific c...