Bounds on singular values revealed by QR factorizations (Q1963915)

This paper deals with bounds on the singular values of a matrix by QR factorizations such a problem had been investigated by \textit{Y. P. Hong} and \textit{C.-T. Pan} [Math. Comput. 58, No. 197, 213-232 (1992; Zbl 0743.65037)] by examining some right singular vectors. By using the pivoting strategy called cyclic pivoting which can be viewed as a generalization of the column pivoting and reverse column pivoting, the QR factorization is proposed. Theoretical analysis and numerical experiments confirm this method and give tight estimates of any two a priori chosen consecutive singular values.