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We consider correspondence analysis (CA) and taxicab correspondence analysis (TCA) of relational datasets that can mathematically be described as weighted loopless graphs. Such data appear in particular in network analysis. We present CA and TCA as relaxation methods for the graph partitioning problem. Examples of real datasets are provided. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates conditions under which an infinite matrix will be bounded as a linear operator between two weighted spaces, and examines the relationship between the matrix and the weight vectors. It is shown that every infinite matrix is bounded as an operator between two weighted spaces, for suitable weights. Necessary conditions and separate sufficient conditions for an infinite matrix to be bounded on some weighted space (with the same weight for its domain and range) are given. We then show a connection between these results and the classical Schur Test which gives a sufficient condition for an infinite matrix to be bounded on the standard (Hilbert) space. [Copyright &y& Elsevier]

Abstract: An approach to the test of the sensor information fusion Kalman filter is proposed. It is based on the introduced statistics of mathematical expectation of the spectral norm of a normalized innovation matrix. The approach allows for simultaneous test of the mathematical expectation and the variance of innovation sequence in real time and does not require a priori information on values of the change in its statistical characteristics under faults. Using this approach, fault detection algorithm for the sensor information fusion Kalman filter is developed. [Copyright &y& Elsevier]

Abstract: Robust exponential stability for interval Cohen–Grossberg neural networks with time varying delay has received increasing interest in recent years. In this paper, some new criteria are derived using linear matrix inequality, matrix norm and Halanay inequality techniques. Compared with the existing results, these new criteria are not conservative and are convenient to check. Three numerical examples are used to show the effectiveness of the obtained results. [Copyright &y& Elsevier]

Let T(bjk) be a finite collection of infinite Toeplitz band matrices, let Tn(bjk) denote their (n + 1) × (n + 1) truncations, and put [This symbol cannot be presented in ASCII format] where . ·. p stands for the operator norm associated with the lp-norm 1 ≤ p < ∝ ) on Cn+1. We establish tight two-sided estimates for the difference Mp - . An. p. It is well known that if T(b) is a Hermitian Toeplitz band matrix and An = Tn(b), then M2 - . An. 2 goes to zero with polynomial speed. We show that such a slow convergence rate is, in a sense, an exceptional case, and we prove that in the generic case Mp - . An. p approaches zero with exponential speed. Our results yield good error estimates when computing the norms of certain infinite matrices via their large truncations and, conversely, when determining the norms of certain large matrices by having recourse to known norms of infinite matrices. [ABSTRACT FROM AUTHOR]