in this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation xa=b to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. as applications, we derive sufficient and necess...

Fast and effective algorithms are discussed for resumming matrix polynomials and Chebyshev matrix polynomials. These algorithms lead to a significant speed-up in computer time by reducing the number of matrix multiplications required to roughly twice the square root of the degree of the polynomial. A few numerical tests are presented, showing that evaluation of matrix functions via polynomial e...

We present methods to compute verified square roots of a square matrix A. Given an approximation X to the square root, obtained by a classical floating point algorithm, we use interval arithmetic to find an interval matrix which is guaranteed to contain the error of X. Our approach is based on the Krawczyk method which we modify in two different ways in such a manner that the computational comp...

-Two new square root Kalman filtering algorithms are presented. Both algorithms are based on the spectral V A of the covariance matrix where V is the matrix whose columns are the eigenvectors of the covariance and A is the diagonal matrix of its eigenvalues. The algorithms use the covariance mode in the time propagation stage and the information mode in the measurement update stage. This switch...

We propose a stable and reduced-complexity detection method for the Bell Labs layered Space-Time (BLAST) coding system. The existing iterative nulling and cancellation algorithm for BLAST has high computational complexity and requires repeated matrix pseudoinverse calculation which may lead to numerical instability. A square-root algorithm was proposed by other researchers to reduce complexity ...

This paper derives a square-root information-type filtering algorithm for nonlinear multi-sensor fusion problems using the cubature Kalman filter theory. The resulting filter is called the square-root cubature Information filter (SCIF). The SCIF propagates the square-root information matrices derived from numerically stable matrix operations and is therefore numerically robust. The SCIF is appl...

Recently we proposed to extend the matrix sign classical iteration to the approximation of the real eigenvalues of a companion matrix of a polynomial and consequently to the approximation of its real roots. In our present paper we advance this approach further by combining it with the alternative square root iteration for polynomials and also show a variation using repeated squaring in polynomi...

We propose topological semimetals generated by the square-root operation for tight-binding models in two and three dimensions, which we call semimetals. The host band touching at finite energies, whose protection is inherited from squared Hamiltonian. Such a character also reflected emergence of boundary modes with energies. Specifically, focusing on properties Hamiltonian class AIII, reveal th...