We address an approximation method for Gaussian process (GP) regression, where we approximate covariance by a block matrix such that diagonal blocks are calculated exactly while off-diagonal blocks are approximated. Partitioning input data points, we present a two-layer hierarchical model for GP regression, where prototypes of clusters in the upper layer are involved for coarse modeling by a GP...

A majorization relating the singular values of an oo-diagonal block of a Hermitian matrix and its eigenvalues is obtained. This basic majorization inequality implies various new and existing results.

In this paper, we present a new approach for the solution to a series of slightly perturbed symmetric eigenvalue problems (A + BSi BT) t = X E, 0 5 i 5 m, where A = AT f 72 nxn, B E 7Znx*, and Si = q E 7ZPx*, p < n. The matrix B is assumed to have full column rank, The main idea of our approach lies in a specific choice of starting vectors used in the block Lanczos algorithm so that the effect ...

In this article, we consider the matrix equation $AXB=C$, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explici...

We determine explicit quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centers and block diagonal forms of these algebras. In the case where q is an arbitrary root of unity, this further determines the degrees.

In this paper, we investigate the stability of some essential spectra a 2x2 block operator matrices pencil with unbounded entries and non-diagonal domain (i.e consisting vectors which satisfy certain relations between their components) by using resolvent kind matrix in terms union restriction its diagonal operators entries. Furthermore, an example two-group transport pencils is presented to ill...

We present an efficient algorithm for computing the permanent for matrices of size N that can written as a product of L block diagonal matrices with blocks of size at most 2. For fixed L, the time and space resources scale linearly in N , with a prefactor that scales exponentially in L. This class of matrices contains banded matrices with banded inverse. We show that such a factorization into a...

In the seismic tomography problem, the subsurface slowness distribution is estimated from the travel-times computed along generally curved rays. For a dense and uniform set of rays, the slowness distribution will be correctly reconstructed. However, for an uneven distribution of rays, the estimated slowness distribution may be influenced by the ray configuration. For the linear case, the seismi...

The row-by-row frontal method may be used to solve general large sparse linear systems of equations. By partitioning the matrix into (nearly) independent blocks and applying the frontal method to each block, a coarse-grained parallel frontal algorithm is obtained. The success of this approach depends on preordering the matrix. This can be done in two stages, (1) order the matrix to bordered blo...

Robust global stabilization of nonlinear systems by observer-based feedback controllers is a challenging task. This article investigates the problem designing stabilizing for incrementally quadratic with external disturbances. The nonlinearities considered in system model satisfy incremental constraints, which are characterized multiplier matrices and encompass many common nonlinearities. simul...