Subspace-based methods have been effectively used to estimate enhanced speech from noisy speech samples. In the traditional subspace approaches, a critical step is splitting of two invariant subspaces associated with signal and noise via subspace decomposition, which is often performed by singular-value decomposition or eigenvalue decomposition. However, these decomposition algorithms are highl...

INCORPORATING KRYLOV SUBSPACE METHODS IN THE ETDRK4 SCHEME by Jeffrey H. Allen The University of Wisconsin–Milwaukee, 2014 Under the Supervision of Professor Bruce Wade A modification of the (2, 2)-Padé algorithm developed by Wade et al. for implementing the exponential time differencing fourth order Runge-Kutta (ETDRK4) method is introduced. The main computational difficulty in implementing th...

It will be shown that extended Krylov subspaces –under some assumptions– can be retrieved without any explicit inversion or system solves involved. Instead we do the necessary computations of A−1v in an implicit way using the information from an enlarged standard Krylov subspace. It is well-known that both for classical and extended Krylov spaces, direct unitary similarity transformations exist...

This is the first of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The non-zero entries in the output are chosen to minimize changes to the singular values and singular vectors corresponding to the near null-space of the input. The output matrix is constrained to preserve left a...

In this paper we study the properties of a kurtosis matrix and propose its eigenvectors as interesting directions to reveal the possible cluster structure of a data set. Under a mixture of elliptical distributions with proportional scatter matrix, it is shown that a subset of the eigenvectors of the fourth-ordermomentmatrix corresponds to Fisher’s linear discriminant subspace. The eigenvectors ...

We study a 1-dimensional AKLT spin chain, consisting of spins S in the bulk and S/2 at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension (S + 1) 2 . This subspace is des...

HAMID HASSANPOUR School of Information Technology and Computer Engineering, Shahrood University of Technology. ___________________________________________________________________________________ Abstract: In this paper, a new method is presented for noise reduction in signal using partial differential equations. In this approach, the signal is initially represented as a matrix. Then using singu...

It is well known that the projection of a matrix A onto a Krylov subspace span { h, Ah, Ah, . . . , Ak−1h } results in a matrix of Hessenberg form. We show that the projection of the same matrix A onto an extended Krylov subspace, which is of the form span { A−krh, . . . , A−2h, A−1h,h, Ah, Ah . . . , A`h } , is a matrix of so-called extended Hessenberg form which can be characterized uniquely ...

Many Krylov subspace methods for shifted linear systems take advantage of the invariance of the Krylov subspace under a shift of the matrix. However, exploiting this fact in the non-Hermitian case introduces restrictions; e.g., initial residuals must be collinear and this collinearity must be maintained at restart. Thus we cannot simultaneously solve shifted systems with unrelated right-hand si...