The performance of standard algorithms for Independent Component Analysis quickly deteriorates under the addition of Gaussian noise. This is partially due to a common first step that typically consists of whitening, i.e., applying Principal Component Analysis (PCA) and rescaling the components to have identity covariance, which is not invariant under Gaussian noise. In our paper we develop the ...

A novel sea mine computer-aided-detection / computer-aided-classification (CAD/CAC) processing string has been developed. The overall CAD/CAC processing string consists of pre-processing, adaptive clutter filtering (ACF), normalization, detection, feature extraction, feature orthogonalization, optimal subset feature selection, classification and fusion processing blocks. The range-dimension ACF...

Nunierically stable and computationally efficient Power System Statc Estimation (PSSE) algorithms are designed using Orthogonalization (QR decomposition) approach. They u3e Givens rotations for orthogonalization which enables sparsity exploitation during factorization of large sparse auginentecl Ja,cobian. Apriori row and column ordering is usiially performed to reduce intermediate a.nd and ove...

We perform error analyses explaining some previously mysterious phenomena arising in numerical computation of the Evans function, in particular (i) the advantage of centered coordinates for exterior product and related methods, and (ii) the unexpected stability of the (notoriously unstable) continuous orthogonalization method of Drury in the context of Evans function applications. The analysis ...

This paper presents a detailed performance analysis of thirdorder nonlinear adaptive systems based on the Wiener model. In earlier work, we proposed the discrete Wiener model for adaptive filtering applications for any order. However, we had focused mainly on first and second-order nonlinear systems in our previous analysis. Now, we present new results on the analysis of third order systems. Al...

A dyadic algorithm for diagonalizing an arbitrary positive definite band matrix, referred to as a Gramian, is obtained efficiently orthogonalize the B-splines. The can be also used fast inversion method Gramian characterized by remarkable sparsity of matrix. There are two versions algorithm: first one more efficient and applicable Toeplitz while second general, works with any but computationall...

In this paper, we extend a recently proposed approach for inverse scattering with Neumann boundary conditions [Druskin et al., Inverse Probl. 37, 075003 (2021)] to the 1D Schrödinger equation impedance (Robin) conditions. This method approaches in two steps: first, extract reduced order model (ROM) directly from data and, subsequently, potential ROM. We also propose novel data-assimilation (DA)...

Important operations in numerical computing are vector orthogonalization. One of the well-known algorithms for vector orthogonalisation is Gram–Schmidt algorithm. This is a method for constructing a set of orthogonal vectors in an inner product space, most commonly the Euclidean space Rn. This process takes a finite, linearly independent set S = {b1, b2, ..., bk} vectors for k ≤ n and generates...