The fuzzy linear regression model with fuzzy input-output data andcrisp coefficients is studied in this paper. A linear programmingmodel based on goal programming is proposed to calculate theregression coefficients. In contrast with most of the previous works, theproposed model takes into account the centers of fuzzy data as animportant feature as well as their spreads in the procedure ofconstr...

We obtain several asymptotic results on the powers of a square matrix associated with SVD, QR decomposition and Cholesky decomposition. 1. Yamamoto’s theorem Given X ∈ Cn×n, the eigenvalue moduli of X are always less than or equal to the spectral norm of X since ‖X‖ := max ‖v‖2=1 ‖Xv‖2 and if Xv = λv for some unit vector v, then |λ| = ‖Xv‖2 ≤ ‖X‖. So for all m ∈ N, r(X) ≤ ‖X‖ ≤ ‖X‖, where r(X) ...

This paper generalizes to the nonlinear case a standard way to solve general sparse systems of linear equations. In particular, Duu 1977] has suggested that row and column interchanges be applied to permute the coeecient matrix of a linear system into block lower triangular form. The linear system then can be solved by using the associated block Gauss-Seidel or forward block substitution scheme...

We obtain an explicit Iwasawa decomposition of the symplectic matrices, complex or real, in terms of the Cholesky factorization for positive definite n×n matrices. We also provide a MATLAB program to compute the decomposition. 1. Iwasawa decomposition of the symplectic groups Let G be the real (noncompact) symplectic group [3, p.129] (the notation there is Spn), [4, p.265] G := Spn(R) = {g ∈ SL...