Existing routines, such as xGELSY or xGELSD in LAPACK, for solving rank-deficient least squares problems require O(mn) operations to solve min ‖b−Ax‖ where A is an m by n matrix. We present a modification of the LAPACK routine xGELSY that requires O(mnk) operations where k is the effective numerical rank of the matrix A. For low rank matrices the modification is an order of magnitude faster tha...

In this paper, we address the problem of joint direction-of-arrival (DoA) and range estimation using frequency diverse coprime array (FDCA). By incorporating structure offsets, a two-dimensional space-frequency virtual difference coarray corresponding to uniform offset is considered increase number degrees-of-freedom (DoFs). However, reconstruction doubly-Toeplitz covariance matrix computationa...

Denote the joint numerical radius of an m-tuple of bounded operators A = (A1, . . . , Am) by w(A). We give a complete description of maps f satisfying w(A − B) = w(f(A) − f(B)) for any two m-tuples of operators A = (A1, . . . , Am) and B = (B1, . . . , Bm). We also characterize linear isometries for the joint numerical radius, and maps preserving the joint numerical range of A. AMS Classificati...

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.

We define the (convex) joint numerical range for an infinite family of compact operators in a Hilbert space H. use this set to determine whether self-adjoint operator A with ±‖A‖ its spectrum is minimal respect diagonals fixed basis E H norm, that ‖A‖≤‖A+D‖, all diagonal D. also describe moment mS=conv{|v|2:v∈S and ‖v‖=1} subspace S⊂H terms ranges obtain equivalences between intersection moment...

The modified Gram–Schmidt algorithm is a well-known and widely used procedure to orthogonalize the column vectors of a given matrix. When applied to ill-conditioned matrices in floating point arithmetic, the orthogonality among the computed vectors may be lost. In this work, we propose an a posteriori reorthogonalization technique based on a rank-k update of the computed vectors. The level of o...