Conditioning of Leverage Scores and Computation by QR Decomposition

QR Factorization Based Blind Channel Identification and Equalization with Second-Order Statistics

Most eigenstructure-based blind channel identification and equalization algorithms with second-order statistics need SVD or EVD of the correlation matrix of the received signal. In this paper, we address new algorithms based on QR factorization of the received signal directly without calculating the correlation matrix. This renders the QR factorization-based algorithms more robust against ill-c...

QR factorization with complete pivoting and accurate computation of the SVD

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...

A DEIM Induced CUR Factorization

We derive a CUR approximate matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix A, such a factorization provides a low rank approximate decomposition of the form A ≈ CUR, where C and R are subsets of the columns and rows of A, and U is constructed to make CUR a good approximation. Given a low-rank singular value decomposition A ≈ VSW , the DEIM p...

Exploratory factor and principal component analyses: some new aspects

Exploratory Factor Analysis (EFA) and Principal Component Analysis (PCA) are popular techniques for simplifying presentation of, and investigating structure of, an (n×p) data matrix. However, these fundamentally different techniques are frequently confused, and the differences between them are obscured, because they give similar results in some practical cases. We therefore investigate conditio...

QR Factorization with Complete Pivotingand Accurate Computation of the SVDNicholas