Complexity reduction of matrix manipulation for multi-user STBC-MIMO decoding

In this paper, we advocate the use of the uncompressed form of i-vector and depend on subspace modeling using probabilistic linear discriminant analysis (PLDA) in handling the speaker and session (or channel) variability. An i-vector is a low-dimensional vector containing both speaker and channel information acquired from a speech segment. When PLDA is used on an i-vector, dimension reduction is performed twice: first in the i-vector extraction process and second in the PLDA model. Keeping the full dimensionality of the i-vector in the i-supervector space for PLDA modeling and scoring would avoid unnecessary loss of information. We refer to the uncompressed i-vector as the i-supervector. The drawback in using the i-supervector with PLDA is the inversion of large matrices in the estimation of the full posterior distribution, which we show can be solved rather efficiently by portioning large matrices into smaller blocks. We also introduce the Gaussianized rank-norm, as an alternative to whitening, for feature normalization prior to PLDA modeling. We found that the i-supervector performs better during normalization. A better performance is obtained by combining the i-supervector and i-vector at the score level. Furthermore, we also analyze the computational complexity of the i-supervector system, compared with that of the i-vector, at four different stages of loading matrix estimation, posterior extraction, PLDA modeling, and PLDA scoring.

This paper focuses on the uplink (UL) of a single-cell massive multiple-input multiple-output (MIMO) systems in which the base station (BS) equipped with M antennas communicates with K single-antenna user equipments (UEs). Due to the finer spatial resolution achieved by a huge number of antennas at the base stations, these systems can substantially reduce intra-cell interference with simple signal processing. However, most precoding schemes exhibit prohibitively high computation complexity as the system dimensions increase. For example, the near-optimal minimum mean squared error (MMSE) precoding requires the inversion of a large matrix. To reduce further the complexity, the truncated polynomial expansion (TPE) is applied to approximate the inverse of large matrices that appear on the expressions of the optimal linear transceivers. A key requirement to achieve good detection performance is to find good polynomial coefficients (J), where the polynomial coefficients (J) are optimized to maximize the system performance. The simulation results show that the proposed scheme provides very close to optimal performance while reducing significantly the computational complexity.

We evaluate imaginary time density-density correlation functions for two-dimensional homogeneous electron gases of up to 42 particles in the continuum using the phaseless auxiliary field quantum Monte Carlo method. We use periodic boundary conditions and up to 300 plane waves as basis set elements. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products, and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems. We discuss the numerical stabilization techniques and the computational complexity of the methodology and we present the limitations related to the size of the systems on a quantitative basis. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of medium-sized homogeneous fermion systems.

A class of Generalized Approximate Inverse Matrix (GAIM) techniques, based on the concept of LU-sparse factorization procedures, is introduced for computing explicitly approximate inverses of large sparse unsymmetric matrices of irregular structure, without inverting the decomposition factors. Explicit preconditioned iterative methods, in conjunction with modified forms of the GAIM techniques, are presented for solving numerically initial/boundary value problems on multiprocessor systems. Application of the new methods on linear boundary-value problems is discussed and numerical results are given.

We consider construction of surrogate models based on variable fidelity samples generated by a high fidelity function an exact representation of some physical phenomenon and by a low fidelity function a coarse approximation of the exact representation. A surrogate model is constructed to replace the computationally expensive high fidelity function. For such tasks Gaussian processes are generally used. However, if the sample size reaches a few thousands points, a direct application of Gaussian process regression becomes impractical due to high computational costs. We propose two approaches to circumvent this difficulty. The first approach uses approximation of sample covariance matrices based on the Nystrom method. The second approach relies on the fact that engineers often can evaluate a low fidelity function on the fly at any point using some blackbox; thus each time calculating prediction of a high fidelity function at some point, we can update the surrogate model with the low fidelity function value at this point. So, we avoid issues related to the inversion of large covariance matrices -- as we can construct model using only a moderate low fidelity sample size. We applied developed methods to a real problem, dealing with an optimization of the shape of a rotating disk.

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

In this paper, a novel reconstruction of the gradient and Hessian tensors on an arbitrary unstructured grid, developed for implementation in a cell‐centered finite volume framework, is presented. The reconstruction, based on the application of Gauss' theorem, provides a fully second‐order accurate estimate of the gradient, along with a first‐order estimate of the Hessian tensor. The reconstruction is implemented through the construction of coefficient matrices for the gradient components and independent components of the Hessian tensor, resulting in a linear system for the gradient and Hessian fields, which may be solved to an arbitrary precision by employing one of the many methods available for the efficient inversion of large sparse matrices. Numerical experiments are conducted to demonstrate the accuracy, robustness, and computational efficiency of the reconstruction by comparison with other common methods. Copyright © 2009 John Wiley & Sons, Ltd.

Reflection and transmission coefficients for an electromagnetic wave are usually computed using the frequency representation: a monochromatic plane wave decomposition [1-2]. Even though this method is a powerful tool, the physical meaning can be hidden by some mathematical complexity coming from Fourier integrals, complex analysis and matrix manipulation. Furthermore, the Maxwell equations, when the fields are only dependent on x and t, are very simple and can be solved using elementary calculation [3]. It will be shown that the physical propagation mechanism, which includes initial conditions, transmission and reflection, can be completely built up within the space-time, rather than in the frequency domain. This would shed a new light on traditional well known results.

K-Nearest Neighbor (KNN) and Support Vector Machine (SVM) are the two Supervised Machine Learning Algorithms which have been used extensively in solving classification and regression problems in various application domains—medical diagnosis, pattern recognition, and image classification being the popular ones. KNN has been attractive for its simplicity—SVM has been considered as complex. Computational complexity of KNN is less compared to SVM. However, accuracy of SVM in general has been higher compared to KNN. This paper carries out an analysis of complexity of KNN and SVM and then looks at the alternative strategies to reduce the complexity. Accuracies of both SVM and KNN are analyzed from literature survey of experimental results with different training datasets. Reduction of number of training instances and usage of kernel functions are found to be the solutions for reducing SVM complexity. Factors impacting KNN accuracy are analyzed and possible alternatives are assessed. Kernel functions and distance-weighted KNN are concluded as the solution to improve KNN accuracy to compete with SVM accuracy. To utilize the best potential of the two algorithms, the option of a hybrid algorithm combining both KNN and SVM is also proposed.

Two new Taylor series approaches are presented for the state space analysis of linear time-invariant delay systems. Both approaches yield an explicit expression for the state vector. This expression involves only the multiplication of matrices of small dimensions. No algebraic system of equations needs to be solved, and therefore no inversion of large matrices is required, as compared to other known techniques. Subsequently, these state space analysis results are used in solving the optimal control problem. The authors' optimal control results give better accuracy. >

Python is a simple, dominant and well-organized interpreted language. Python is used to develop the very high performance scientific related application and it is used to develop an application for Numeric computation, it is frequently used. Using python we can develop a high performance applications Python often utilizes external libraries to perform scientific computing. The most important libraries used are NumPy, SciPy and Matplotlib to perform scientific and numeric applications. The Python libraries are open-source tag-on modules, which do additional frequent mathematical and numerical routines in pre-compiled, high-speed tasks. These two modules are providing the functionality that meets, or perhaps exceeds, that related with common commercial software like MATLAB. The python package NumPy (Numeric Python) is used for manipulating large arrays and matrices of numeric data. The Scientific Python (SciPy) extends the functionality of NumPy with a considerable collection of valuable algorithms, like minimization, Fourier transformation, regression, and other applied mathematical techniques.Matrix Laboratory (MATLAB) is a multiple programming paradigm. it is used for numerical computing environment and it is a proprietary programming language. The following various operations are performed by the MATLAB, operations are plotting of functions and data, matrix manipulations, python use an interface for user to interact with an application, some type of algorithms are used for implementation purpose and another type of programming languages are used to create interfacing with programs. The combination of the following three packages NumPy, SciPy and Matplotlib/Pylab are alternatively used as a MATLAB, so this three packages give the alternative to MATLAB, MATLAB environment is best suit for scientific works. Python provide a alternative to MATLAB.

The power networks of nongrounded DC traction systems are generically longitude ladder-like circuits. The solution of DC power flow for such circuits using nodal analysis requires manipulation of large conductance matrix and Jacobian matrix. We present an approach that decomposes the whole network into individual ladder circuits and employs the chain rule to reduce the Jacobian matrices into the product of a sequence of derivatives. Thus we can solve the DC power flow iteratively without dealing with large matrices, making it simple and efficient for either manual or computer calculation.

In this paper we review the application of wavelets to the solution of partial differential equations. We consider in detail both the single scale and the multiscale Wavelet Galerkin method. The theory of wavelets is described here using the language and mathematics of signal processing. We show a method of adapting wavelets to an interval using an extrapolation technique called Wavelet Extrapolation. Wavelets on an interval allow boundary conditions to be enforced in partial differential equations and image boundary problems to be overcome in image processing. Finally, we discuss the fast inversion of matrices arising from differential operators by preconditioning the multiscale wavelet matrix. Wavelet preconditioning is shown to limit the growth of the matrix condition number, such that Krylov subspace iteration methods can accomplish fast inversion of large matrices.

This paper investigates the issue of direction finding of multiple signals using coprime array with sensor gain and phase errors. As the sensor errors decrease the performance of direction estimation, it proposes a calibration method with one signal, where one accurate direction signal enables to obtain high precise result. By building the rough direction signal in real system as usual, it introduces the gain self-calibration and iterative self-calibration to enhance the performance of error estimation, which is based on the rough error estimate by one signal calibration. Considering the analysis of computational complexity and performance simulation, the gain self-calibration improves the performance in low signal to noise ratio compared with no self-calibration and the iterative self-calibration gets the best performance with the most computational complexity. With known error values, it can be found more signals than the sensor number with coprime array.

The electromagnetic scattering problem over a wide incident angle can be rapidly solved by introducing the compressive sensing theory into the method of moments, whose main computational complexity is comprised of two parts: a few calculations of matrix equations and the recovery of original induced currents. To further improve the method, a novel construction scheme of measurement matrix is proposed in this paper. With the help of the measurement matrix, one can obtain a sparse sensing matrix, and consequently the computational cost for recovery can be reduced by at least half. The scheme is described in detail, and the analysis of computational complexity and numerical experiments are provided to demonstrate the effectiveness.