We propose an implementation of the data structure presented by Kaplan, Mozes, Nussbaum, and Sharir in [KMNS12] for submatrix maximum queries in Monge matrices. The implementation shows that the average running time of the algorithm is similar to the proved worse case running time: O(log n). We also propose a new efficient and low-memory consuming procedure to generate random Monge matrices.

We explore the size of the largest (permuted) triangular submatrix of a random matrix, and more precisely its asymptotical behavior as the size of the ambient matrix tends to infinity. The importance of such permuted triangular submatrices arises when dealing with certain combinatorial algebraic settings in which these submatrices determine the rank of the ambient matrix, and thus attract a spe...

An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.

We present an algorithm for solving linear systems involving the probability or rate matrix for a Markov chain. It is based on a UL factorization but works only with a submatrix of the factor U. We demonstrate its utility on Erlang-B models as well as more complicated models of a telephone multiplexing system.

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...

This paper introduces a new (dis)similarity measure for 2D arrays, extending the Average Common Submatrix measure. This is accomplished by: (i) considering the frequency of matching patterns, (ii) restricting the pattern matching to a fixed-size neighborhood, and (iii) computing a distance-based approximate matching. This will achieve better performances with low execution time and larger infor...

Let a, b be fixed positive integers. It is proved that if every relatively large sub-matrix of a i-l-matrix N contains about the same number of both entries, then all 2 " b a by b matrices occur asymptotically the same number of times as a submatrix of N. A similar statement is shown to hold for graphs with uniformly distributed edges.

Principal component analysis and evolving factor analysis were applied to the study of the speciation of Cu (II)/ethylenediamine/ oxalate. Two programs were designed, based on mathematical algorithms. Error functions were calculated for evaluating the number of species. Submatrix analysis plots were constructed to estimate the species present in the system. The method should prove useful in stu...

A simple and straightforward formula for computing the inverse of a submatrix in terms of the inverse of the original matrix is derived. General formulas for the inverse of submatrices of order n − k as well as block submatrices are derived. The number of additions (or subtractions) and multiplications (or divisions) on the formula is calculated. A variety of numerical results are shown.

We consider two closely related problems: planted clustering and submatrix localization. In the planted clustering problem, a random graph is generated based on an underlying cluster structure of the nodes; the task is to recover these clusters given the graph. The submatrix localization problem concerns locating hidden submatrices with elevated means inside a large real-valued random matrix. O...