A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...

Abstract Expectiles are the solution to an asymmetric least squares minimization problem for univariate data. They resemble quantiles, and just like them, expectiles indexed by a level ? in unit interval. In present paper, we introduce discuss main properties of (multivariate) expectile regions, nested family sets, whose instance with 0 ? 1 ? 2 is built up all points projections lie between lev...

The matrix functions appear in several applications in engineering and sciences. The computation of these functions almost involved complicated theory. Thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. The aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. More...