As we know, unextendible product basis (UPB) is an incomplete basis whose members cannot be perfectly distinguished by local operations and classical communication. However, very little is known about those incomplete and locally indistinguishable product bases that are not UPBs. In this paper, we first construct a series of orthogonal product bases that are completable but not locally distingu...

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some...

H–bases are bases for polynomial ideals, characterized by the fact that their homogeneous leading terms are a basis for the associated homogeneous ideal. In the computation of H–bases without term orders, an important task is to determine the orthogonal projection of a homogeneous polynomial to certain subspaces of homogeneous polynomials with respect to a given inner product. One way of doing ...

Wavelet Analysis provides a new orthogonal basis set which is localized in both physical space and Fourier transform space. Empirical Orthogonal Functions (EOFs), on the other hand, provide a global representation of data sets. Here we investigate the various ways in which one can combine these basis sets for optimal representation of data. EOFs represent the global large scale information and ...

Orthogonal and Symmetric Haar Wavelets on the Sphere Christian Lessig Master of Science Graduate Department of Computer Science University of Toronto 2007 The efficient representation of signals defined over spherical domains has many applications. We derive a new spherical Haar wavelet basis (SOHO) that is both orthogonal and symmetric, rebutting previous work that presumed the nonexistence of...

For a general vector space V , and a linear operator T , we have already asked the question “when is there a basis of V consisting only of eigenvectors of T?” – this is exactly when T is diagonalizable. Now, for an inner product space V , we know how to check whether vectors are orthogonal, and we know how to define the norms of vectors, so we can ask “when is there an orthonormal basis of V co...

An adaptive model reduction method is proposed for linear timeinvariant systems based on the continuous-time rational orthogonal basis (TakenakaMalmquist basis). The method is to find an adaptive approximation in the energy sense by selecting optimal points for the rational orthogonal basis. The stability of the reduced models holds, and the steady-state values of step responses are kept to be ...

In Compressed Sensing (CS) framework, reconstruction of a signal relies on the knowledge of the sparse basis & measurement matrix used for sensing. Most of the studies so far focus on the application of CS in fields of images, radar, astronomy and Speech. This paper introduce new approach called combined basis that is made by separating voiced and unvoiced parts and applying different basis for...

Orthogonal and Symmetric Haar Wavelets on the Sphere Christian Lessig Master of Science Graduate Department of Computer Science University of Toronto 2007 The efficient representation of signals defined over spherical domains has many applications. We derive a new spherical Haar wavelet basis (SOHO) that is both orthogonal and symmetric, rebutting previous work that presumed the nonexistence of...

Orthogonal and Symmetric Haar Wavelets on the Sphere Christian Lessig Master of Science Graduate Department of Computer Science University of Toronto 2007 The efficient representation of signals defined over spherical domains has many applications. We derive a new spherical Haar wavelet basis (SOHO) that is both orthogonal and symmetric, rebutting previous work that presumed the nonexistence of...