The Nyström method is an efficient technique for the eigenvalue decomposition of large kernel matrices. However, to ensure an accurate approximation, a sufficient number of columns have to be sampled. On very large data sets, the singular value decomposition (SVD) step on the resultant data submatrix can quickly dominate the computations and become prohibitive. In this paper, we propose an accu...

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 a novel technique for Image Authentication in Frequency Domain using Discrete Fourier Transformation Technique (IAFDDFTT) has been proposed to authenticate a gray level PGM, TIFF image by embedding a message/image where 2 x 2 submatrix is taken as source matrix from the image matrix and transform into the frequency domain. Two bits of authenticating message/image are fabricated wi...

We show that a unitary upper Hessenberg matrix with positive subdiago-nal elements is uniquely determined by its eigenvalues and the eigenvalues of a modiied principal submatrix. This provides an analog of a well-known result for Jacobi matrices.

De ne the perrank of a matrix A to be the size of a largest square submatrix of A with nonzero permanent. Motivated in part by the Alon-Jaeger-Tarsi Conjecture [3], we prove several results on perranks.

The Nyström method is an efficient technique for the eigenvalue decomposition of large kernel matrices. However, in order to ensure an accurate approximation, a sufficiently large number of columns have to be sampled. On very large data sets, the SVD step on the resultant data submatrix will soon dominate the computations and become prohibitive. In this paper, we propose an accurate and scalabl...

We investigate the extent to which eigenstate thermalization hypothesis (ETH) is valid or violated in nonintegrable and integrable spin-$1/2 XXZ$ chains. perform energy-resolved analysis of statistical properties matrix elements observables energy basis. The Hilbert space divided into shells constant width, a block submatrix constructed whose columns rows correspond eigenstates respective shell...

This paper studies the minimax detection of a small submatrix of elevated mean in a p× p matrix contaminated by additive Gaussian noise where p tends to infinity. To investigate the tradeoff between statistical performance and computational cost from a complexity-theoretic perspective, we consider a sequence of discretized models which are asymptotically equivalent in the sense of Le Cam. Under...

In this literature, the symmetric inverse generalized eigenvalue problem with submatrix constraints and its corresponding optimal approximation problem are studied. A necessary and sufficient condition for solvability is derived, and when solvable, the general solutions are presented.