Consider the powers of a square matrix A of order n in bottleneck algebra, where addition and multiplication are replaced by the max and min operations. The powers are periodic, starting from a certain power AK . The smallest such K is called the exponent of A and the length of the period is called the index of A. Cechlárová has characterized the matrices of index 1. Here we consider the case w...

In this paper , the concept of the partition anti-circulant matrix on skew field is given,and its operational properties is discussed. Mathematics Subject Classification: 15A24

The numerical solution of large and sparse nonsymmetric linear systems of algebraic equations is usually the most time consuming part of time-step integrators for differential equations based on implicit formulas. Preconditioned Krylov subspace methods using Strang block circulant preconditioners have been employed to solve such linear systems. However, it has been observed that these block cir...

Polynomial based methods have recently been used in several works for mitigating the effect of stragglers (slow or failed nodes) distributed matrix computations. For a system with $n$ worker nodes where notation="LaTeX">$s$ can be stragglers, these approaches allow an optimal recovery threshold, whereby intended result dec...

In this paper, by considering the g-circulant matrix Cn,g(H) = gcirc(Hk,1,Hk,2, . . . ,Hk,n) whose entries are the generalized k-Horadam numbers, we present a new generalization to compute spectral norm, determinant and inverse of Cn,g(H). In fact the results in here are the most general statements to obtain the inverses and determinants in such matrices having the elements of all second order ...

The zero forcing number of a graph G is the cardinality of the smallest subset of the vertices of G that forces the entire graph using a color change rule. This paper presents some basic properties of circulant graphs and later investigates zero forcing numbers of circulant graphs of the form C[n, {s, t}], while also giving attention to propagation time for specific zero forcing sets.

A class of supersaturated designs called k-circulant designs is explored. These designs are constructed from cyclic generators by cycling k elements at a time. The class of designs includes many Es2-optimal designs, some of which are already known and some of which are more efŽ cient than known designs for model estimation under factor sparsity. Generators for the most efŽ cient designs are lis...

A fast solution algorithm is proposed for solving block banded block Toeplitz systems with non-banded Toeplitz blocks. The algorithm constructs the circulant transformation of a given Toeplitz system and then by means of the Sherman-Morrison-Woodbury formula transforms its inverse to an inverse of the original matrix. The block circulant matrix with Toeplitz blocks is converted to a block diago...