Lanczos vectors computed in nite precision arithmetic by the three-term recurrence tend to lose their mutual biorthogonality. One either accepts this loss and takes more steps or re-biorthogonalizes the Lanczos vectors at each step. For the symmetric case, there is a compromise approach. This compromise, known as maintaining semi-orthogonality, minimizes the cost of re-orthogonalization. This p...

This paper deals with a new technique for multi-channel separation of speech signals from convolutive mixtures under coherent noise. We demonstrate how the scaled transfer functions from the sources to the microphones can be estimated even in the presence of stationary coherent noise. The key to this are generalized eigenvalue decompositions of the power spectral density (PSD) matrices of the n...

Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.

Last time we defined the minimum distance λ1(L) of a lattice L, and showed that it is upper bounded by √ n · det(L)1/n (Minkowski’s theorem), but this bound is often very loose. Some natural computational questions are: given a lattice (specified by some arbitrary basis), can we compute its minimum distance? Can we find a vector that achieves this distance? Can we find good approximations to th...

Abstract Our aim in this paper is presenting an attractive numerical approach giving accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed Caputo–Fabrizio derivative. By means of such approach, we utilize Gram–Schmidt orthogonalization process create orthonormal set bases that leads appropriate Hilbert space $\mathcal...

In conventional hybrid beamforming approaches, the number of radio-frequency (RF) chains is bottleneck on achievable spatial multiplexing gain. Recent studies have overcome this limitation by increasing update-rate RF beamformer. This paper presents a framework to design and evaluate such which we refer as agile beamforming, from theoretical practical points view. context, consider impact RF-ch...

Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets, the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from loss of orthogonality, and therefore its applicability is usually limited to the estimation of the first few components. Here we present an algorithm based on ...

NTRU is a very efficient public-key cryptosystem based on polynomial arithmetic. Its security is related to the hardness of lattice problems in a very special class of lattices. This article is motivated by an interesting peculiar property of NTRU lattices. Namely, we show that NTRU lattices are proportional to the so-called symplectic lattices. This suggests to try to adapt the classical reduc...

This paper presents a method for reducing the number of rules for large rule based fuzzy systems. While retaining the linguistic information of the original system, the reduction is achieved by attempting to select the most significant rules that have important contribution in the error reduction. Using a numerically efficient modified Gram-Schmidt orthogonalization routine, a measure called ru...

Blind adaptive beamforming is often used in communication systems to combat co-channel interference. Among a number of techniques, the constant modulus algorithm (CMA) has proven to be an e ective tool for blind beamforming of uncorrelated signals. Unfortunately, CMA beamformers encounter problems for correlated signals and interferences. In this paper, we consider correlated co-channel input s...