We discuss a method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part of a new computational approach wh...

Abstract. Integrability, algebraic structures and orthogonal basis of the Calogero model are studied by the quantum Lax and Dunkl operator formulations. The commutator algebra among operators including conserved operators and creation-annihilation operators has the structure of the W-algebra. Through an algebraic construction of the simultaneous eigenfunctions of all the commuting conserved ope...

Inverting the distortion of signals and images in presence of additive noise is often numerically unstable. To solve these ill-posed inverse problems, we study linear and non-linear diagonal estimators in an orthogonal basis. General conditions are given to build nearly minimax optimal estimators with a thresholding in an orthogonal basis. As an application, we study the deconvolution of bounde...

A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand–Tsetlin patterns. The basis is consistent with the chain of subalgebras g1 ⊂ · · · ⊂ gn, where gk = o(2k). Explicit formulas for the matrix elements of generators of o(2n) in this basis are given. The construction is b...

This paper aims to develop a novel framework to systematically trade-off computational complexity with output distortion in linear multimedia transforms, in an optimal manner. The problem is important in real-time systems where the computational resources available are time-dependent. We solve the real-time adaptation problem by developing an approximate transform framework. There are three key...

We examine a certain class of Schauder bases for the space C[−1, 1] consisting of algebraic polynomials orthogonal with respect to the Chebycheff weight of the first kind. We give an improved estimate for its Lebesgue constants.

Multiresolution Approximation subspaces are L2(R)-subspaces defined for each scale over all time shifts, i.e., “scale subspaces”, while with respect to a given wavelet, the signal space L2(R) not only admits orthogonal scale subspaces basis, but orthogonal “time shift subspaces” basis as well. It is therefore natural to expect both scale subspaces and time shift subspaces to play a role in Wave...

In this paper, we present a technique for estimating the input nonlinearity of a Hammerstein system by using multiple orthogonal ersatz nonlinearities. Theoretical analysis shows that by replacing the unknown input nonlinearity by an ersatz nonlinearity, the estimates of the Markov parameters of the plant are correct up to a scalar factor, which is related to the inner product of the true input...

We prove that if a lattice basis is nearly orthogonal (the angle between any basis vector and the linear subspace spanned by the other basis vectors is at least π3 radians), then a KZ-reduced basis can be obtained from it in polynomial time. We also show that if a nearly orthogonal lattice basis has nearly equal vector lengths (within a certain constant factor of one another), then the basis is...