The development of accurate and fast numerical schemes for the five-fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-...
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The development of accurate and fast numerical schemes for the five-fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres model in dimension three, we are able to derive spectral methods that can be evaluated through fast algorithms. These algorithms are based on a suitable representation and approximation of the collision operator. Explicit expressions for the errors in the schemes are given and spectral accuracy is proved. Parallelization properties and adaptivity of the algorithms are also discussed.
The problem of numerical solution of a nonlinear Schrodinger equation is considered from the point of view of applications to the compensation of signal distortions in a fiber optic communication line. The problem of ...
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The problem of numerical solution of a nonlinear Schrodinger equation is considered from the point of view of applications to the compensation of signal distortions in a fiber optic communication line. The problem of constructing fast algorithms for the direct and inverse scattering problems for the Zakharov-Shabat system of equations is studied. An overview of the main methods used currently is given. The time complexity of the algorithms is described together with their applicability to realistic signals.
In the paper, fast algorithms for three short prime length fast biased polynomial transforms are presented, based on the strategy of the minimum number of rotations. These algorithms are of practical use in digital im...
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In the paper, fast algorithms for three short prime length fast biased polynomial transforms are presented, based on the strategy of the minimum number of rotations. These algorithms are of practical use in digital image processing.
The classical algorithms require order n3 operations to compute the first n terms in the reversion of a power series or the composition of two series, and order nelog n operations if the fast Founer transform is used ...
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Two types of efficient algorithms for fast implementation of the 2-D discrete cosine transform (2-D DCT) are developed. One involves recursive structure which implies that the algorithm for (M/2 X N/2) block be extend...
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Two types of efficient algorithms for fast implementation of the 2-D discrete cosine transform (2-D DCT) are developed. One involves recursive structure which implies that the algorithm for (M/2 X N/2) block be extended to (M X N/2) (M/2 X M) and (M X N) blocks (M and N are integer powers of two). The second algorithm is nonrecursive and therefore it has to be tailored for each block size. Both algorithms involve real arithmetic and they reduce the number of multiplications significantly compared to the fast algorithm developed by Chen et al. [8], while the number of additions remain unchanged.
This paper deals with efficient triangularization, inversion and system solution of block Toeplitz matrices with Toeplitz entries. fast algorithms are developed which taking into advantage the joint Toeplitz structure...
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This paper deals with efficient triangularization, inversion and system solution of block Toeplitz matrices with Toeplitz entries. fast algorithms are developed which taking into advantage the joint Toeplitz structure, reduce by a factor of two the complexity of existing algorithms for general block Toeplitz matrices. Zusammenfassung Dieser Beitrag beschreibt efficiente Triangularization, Invertierung und Lösung von Systemen bestehend aus Block Toeplitz Matrizen mit Toeplitz Elementen. Schnelle Algorithmen werden eingeführt die, basierend auf der doppel Toeplitz Struktur, die Komplexität von existierenden Algorithmen für allgemeine Toeplitz Matrizen um einen Faktor 2 reduzieren.
The reverberation time (RT) measures the persistence of a sound in enclosed acoustic spaces. In a previous work, a method for the blind maximum-likelihood estimation (MLE) of RT using passively received microphone sig...
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The reverberation time (RT) measures the persistence of a sound in enclosed acoustic spaces. In a previous work, a method for the blind maximum-likelihood estimation (MLE) of RT using passively received microphone signals was presented. The procedure overcomes the drawbacks of current methods that use a controlled sound source for RT determination. Here, fast algorithms for online implementation of the method are developed. One algorithm, suitable for a one-time determination of the RT, requires O(N) computations for a data frame of length N. A second IIR algorithm, based on Q-levels of quantization, requires O(Q) computations. Results for speech data and choice of algorithms are discussed.
This paper presents computationally efficient implementations for Iterative Adaptive Approach (IAA) spectral estimation techniques for uniformly sampled data sets. By exploiting the methods inherent low displacement r...
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ISBN:
(纸本)9781457705397
This paper presents computationally efficient implementations for Iterative Adaptive Approach (IAA) spectral estimation techniques for uniformly sampled data sets. By exploiting the methods inherent low displacement rank, together with the development of suitable Gohberg-Semencul representations, and the use of data dependent trigonometric polynomials, the proposed implementations are shown to offer a reduction of the necessary computational complexity with at least one order of magnitude. Numerical simulations together with theoretical complexity measures illustrate the achieved performance gain.
Hyperspectral endmember extraction (EE) is to estimate endmember signatures (or material spectra) from the hyperspectral data of an unexplored area for analyzing the materials and their composition therein. However, t...
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ISBN:
(纸本)9781467300469
Hyperspectral endmember extraction (EE) is to estimate endmember signatures (or material spectra) from the hyperspectral data of an unexplored area for analyzing the materials and their composition therein. However, the presence of noise in the data posts a serious problem for EE. Recently, robustness against noise has been taken into account in the design of EE algorithms. The robust maximum-volume simplex criterion [1] has been shown to yield performance improvement in the noisy scenario, but its real applicability is limited by its high implementation complexity. In this paper, we propose two fast algorithms to approximate this robust criterion [1], which turns out to deal with a set of partial max-min optimization problems in alternating manner and successive manner, respectively. Some Monte Carlo simulations demonstrate the superior computational efficiency and efficacy of the proposed robust algorithms in the noisy scenario over the robust algorithm in [1] and some benchmark EE algorithms.
In this paper is presented a class of stochastic signals and of correlation matrices introducing very fast algorithms for solving linear problems. These signals are derived from white noise by using three kinds of ope...
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In this paper is presented a class of stochastic signals and of correlation matrices introducing very fast algorithms for solving linear problems. These signals are derived from white noise by using three kinds of operations combined in various orders: summation, difference and instantaneous modulation. The discrete time Brownian motion is a particular example of such signals. Zusammenfassung Dieser Beitrag beschreibt eine Klasse von stochastischen Signalen und Korrelationsmatrizen, die die Anwendung sehr schneller Algorithmen zur Lösung linearer Probleme gestatten. Mit Hilfe dreier Rechenoperationen—der Summierung, der Differenzbildung und der gedächtnisfreien Modulation, die sich in verschiedener Reihenfolge kombinieren lassen—werden diese Signale aus weißem Rauschen erzeugt. Die (abgetastete) Brownsche Molekularbewegung ist ein besonderes Beispiel derartiger Signale.
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