Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called rank-revealing QR, which seeks a well-conditioned collection of columns that spans the (numerical) range of the matrix. The functional analysis literature contains a...

We introduce the following hidden hubs model H(n, k, σ0, σ1): the input is an n × n random matrix A with a subset S of k special rows (hubs); entries in rows outside S are generated from the Gaussian distribution p0 = N(0, σ 0), while for each row in S, an unknown subset of k of its entries are generated from p1 = N(0, σ 1), σ1 > σ0, and the rest of the entries from p0. The special rows with hi...

For a given selection of rows and columns from Fourier matrix, we give number tests for whether the resulting submatrix is Hadamard based on primitive sets those columns. In particular, demonstrate that matrix forms exactly determined by are compatible with respect to size matrix. This allows partitioning all submatrices into equivalence classes will consist entirely or non-Hadamard motivates c...

A clan is a compact connected topological semigroup with identity. Professor A. D. Wallace has raised the following question [9]: Is a clan of real »X» matrices with non-negative entries, which contains the identity matrix, necessarily acyclic? That is to say, do all of the Alexander-Cech cohomology groups with arbitrary coefficients (in positive dimensions) vanish? In this paper the slightly s...

The job rotation problem (JRP) is the following: Given an n × n matrix A over R ∪ {−∞} and k ≤ n, find a k × k principal submatrix of A whose optimal assignment problem value is maximum. No polynomial algorithm is known for solving this problem if k is an input variable. We analyse JRP and present polynomial solution methods for a number of special cases.

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in a n inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the co...

We propose an accelerated density matrix purification scheme with error control. The method makes use of the scale-and-fold acceleration technique and screening submatrix products in block-sparse matrix-matrix multiplies to reduce computational cost. An bound a parameter sweep are combined select threshold value for screening, such that can be controlled. evaluate performance comparison without...

Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called rank-revealing QR, which seeks a well-conditioned collection of columns that spans the (numerical) range of the matrix. The functional analysis literature contains a...

In this paper we consider the Order Preserving Submatrix (OPSM) problem. This problem is known to be NP -hard. Although in recent years some heuristic methods have been presented to find OPSMs, they lack the guarantee of optimality. We present exact solution approaches based on linear mixed 0–1 programming formulations, and develop algorithmic enhancements to aid in solvability. Encouraging com...