Parametrization of filters on the basis of orthonormal basis functions have been widely used in system identification and adaptive signal processing. The main advantage of using orthonormal basis functions for a filter parametrization lies in the possibility of incorporating prior knowledge of the system dynamics into the identification process and adaptive signal process. As a result, a more a...

Frisvad [2012b] describes a widely-used computational method for efficiently augmenting a given single unit vector with two other vectors to produce an orthonormal frame in three dimensions, a useful operation for any physically based renderer. However, the implementation has a precision problem: as the z component of the input vector approaches −1, floating point cancellation causes the frame ...

Entailment is a logical relationship in which the truth of a proposition implies the truth of another proposition. The ability to detect entailment has applications in IR, QA, and many other areas. This study uses the vector space model to explore the relationship between cohesion and entailment. A Latent Semantic Analysis space is used to measure cohesion between propositions using vector simi...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

An orthonormal basis matrix $ X of a subspace {\mathcal X} is known not to be unique, unless there are some kinds normalization requirements. One them require that X^{ \text{T}}D positive semi-definite, where D constant apt size. It natural one in multi-view learning models which serves as projection and determined by maximization problem over the Stiefel manifold whose objective function conta...

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also dene the concepts of bessel, hilbert ov-basis and obt...