Continued Fraction Expansions of Matrix Eigenvectors

On the real quadratic fields with certain continued fraction expansions and fundamental units

The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element  where $dequiv 2,3( mod  4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and  $n_d$ and $m_d...

A matrix Euclidean algorithm and matrix continued fraction expansions

The Random Continued Fraction Transformation

We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.

EIGENVECTORS OF COVARIANCE MATRIX FOR OPTIMAL DESIGN OF STEEL FRAMES

In this paper, the discrete method of eigenvectors of covariance matrix has been used to weight minimization of steel frame structures. Eigenvectors of Covariance Matrix (ECM) algorithm is a robust and iterative method for solving optimization problems and is inspired by the CMA-ES method. Both of these methods use covariance matrix in the optimization process, but the covariance matrix calcula...

On The Khintchine Constant For Centred Continued Fraction Expansions∗

In this note, we consider a classical constant that arises in number theory, namely the Khintchine constant. This constant is closely related to the growth of partial quotients that appear in continued fraction expansions of reals. It equals the limit of the geometric mean of the partial quotient which is proved to be the same for almost all real numbers. We provide several expressions for this...