Scaled iterates associated with the serial Kogbetliantz method for computing the singular value decomposition (SVD) of complex triangular matrices are considered. They are defined by B (k) S = |diag(B )| B |diag(B)|, where B are matrices generated by the method. Sharp estimates are derived for the Frobenius norm of the off-diagonal part of B (k) S , in the case of simple singular values. This n...

This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of Métivier and Pellaumail which is quite restrictive. We make use of the notion of χ-covariation which is a generalized notion of covariation for processes with values in two Banach spaces B1 and B2. χ refers to a suitable subspace of the dual ...

The complex dynamical analysis of the cubic-order iterative family is proposed to draw fractal images via M\"{o}bius conjugacy map applied a quadratic polynomial $(z-A) (z-B)$. resulting dynamics clearly visualized through various stability surfaces and parameter spaces using Mathematica.

Let t be an integer taking on values between 1 and x (x real), let irhc(t) denote the number of positive primes < t which are s c (mod b), and let li t denote the usual integral logarithm of /. Further, let the ratio of quadratic nonresidues of b > 2 to quadratic residues of bbey(b) to 1, and let l/ * * , Ah(x) = (i/y(b))-\ £ n.c(0-r(») L "i,X>)\ M<c<*-1 l«c'<Ä-l ' where c runs over quadratic n...

Introduction: The ability of quadratic dose protocol to maintain a good quality image for an overweight and obese patient is well reported. However, a practical approach to the implementation of this protocol in whole-body imaging in Malaysia is currently lacking. Hence, the aim of this study is to derive the quadratic dose formula that suits our PET system. Metho...

In this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. First we introduce a parametric equivalent of the problem. Then a bisection and a generalized Newton-based method algorithms are presented to solve it. In order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function φ(Z) = Q − ZPZ′ is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this ...

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B → 2B) and a cubic (A+ 2B → 3B) autocatalysis. The parameters of this system are the ratio D = DB/DA of the diffusion constants of the reactant A and the autocatalyst B, and the relative activity k of the cubic reaction. First, for all values of D >...

We present the construction of a multivariate normalized B-spline basis for the quadratic C-continuous spline space defined over a triangulation in R (s ≥ 1) with a generalized Powell-Sabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction can be interpreted geometrically as the determination of a set of s-simplices ...