A bounded linear operator acting on a Hilbert space is a generalized quadratic operator if it has an operator matrix of the form [ aI cT dT ∗ bI ] . It reduces to a quadratic operator if d = 0. In this paper, spectra, norms, and various kinds of numerical ranges of generalized quadratic operators are determined. Some operator inequalities are also obtained. In particular, it is shown that for a...

We characterize under what conditions n×n Hermitian matrices A1 and A2 have the property that spectrum of cos⁡tA1+sin⁡tA2 is independent t (thus, trigonometric pencil isospectral). One characterizations requires first ⌈n2⌉ higher rank numerical ranges matrix A1+iA2 to be circular disks with center 0. Finding unitary similarity between and, say, involves finding a solution Lax's equation.

polymer-clay nano-composite materials, in which nano-meter thick layers of clay dispersed in polymer matrix, have generally higher mechanical properties than normal polymeric materials. a new three-dimensional unit cell model has been developed for modeling three constituent phases including inclusion, interphase and matrix. the total elastic modulus of nano-composite is evaluated.  numerical r...

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a of that is nonnegative, but whose factors can be arbitrary. calculate computational complexities proposed methods and evaluate their performance in numerical experiments. The comparison with known deterministic shows approaches are faster ex...