Unitary Triangularization of a Nonsymmetric Matrix

Householder, A. S.

doi:10.1145/320941.320947

Cited by 507 publications

(236 citation statements)

References 2 publications

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“…In [1], HOUSEHOLDER stressed the use of orthogonal transformations for solving linear least squares problems. In this paper, we shall exploit these transformations.…”

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confidence: 99%

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Numerical methods for solving linear least squares problems

1965

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“…In [1], HOUSEHOLDER stressed the use of orthogonal transformations for solving linear least squares problems. In this paper, we shall exploit these transformations.…”

mentioning

confidence: 99%

“…A very effective method to realize the decomposition (4) is via Householder transfor mations [1]. Let A = A (1) , and let A (2) , A (3) , ..., A…”

mentioning

confidence: 99%

Numerical methods for solving linear least squares problems

1965

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“…The QR decomposition of a matrix always exists [18], even if the matrix does not have a full rank. To find the QR decomposition, the Householder transformation (called also Householder reflection) [19] can be used. This brings to the final relation: • n(N x +1)+(n+1) operations for the output calculation;…”

Section: B Modification Of the Mlmvn Learning Algorithm Using Complementioning

confidence: 99%

Analog system modeling based on a double modified complex valued neural network

Luchetta

Manetti

Piccirilli

2013

The 2013 International Joint Conference on Neural Networks (IJCNN)

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Abstract-The aim of this work is to present a novel technique for the identification of lumped circuit models of general distributed apparatus and devices. It is based on the use of a double modified complex value neural network. The method is not oriented to a unique class of electromagnetic systems, but it gives a procedure for the complete validation of the approximated lumped model and the extraction of the electrical parameter values. The inputs of the system are the geometrical (and/or manufacturing) parameters of the considered structure, while the outputs are the lumped circuit parameters. The method follows the Frequency Response Analysis (FRA) approach for elaborating the data presented to the network. I. INTRODUCTIONURING the analog circuit design process, in many cases the phase of modelization, parameter identification and simulation of distributed circuits is still an arduous challenge. The difficulties are inherent in locating the parameters that can be extracted and in obtaining the requested precision for them. On the other hand, this phase can become essential to solve several problems, as, for example, the study of the transient part of the response, the evaluation of the electromagnetic compatibility, the estimate of the harmonic content, the detection and location of faults, the influence of a single parameter over the output final behavior. In the last few years several soft computing algorithms dealing with this subject have been developed, using artificial neural networks (ANNs) [1][2][3], genetic algorithms (GAs) [4,5], particle swarm optimizers (PSOs) [6,7].In this paper we propose a new neural architecture able to accomplish the identification task. It is constituted by the union of a pair of multi-valued neuron neural networks with complex weights [8]. In this kind of architecture it is possible to use a set of multifrequency measurements or simulations made on the device, taken at different values of geometrical parameters, and train a MultiLayer Multi-Valued Neuron Network (MLMVN), able to estimate the electrical parameters of the lumped model. A single network is not A. Luchetta is with the Dipartimento di Ingegneria dell'Informazione (DINFO) of the University of Florence, Via S.Marta, 3, 50139 Firenze, Italy (phone: +39-055-4796461; fax: +39-055-4796442; e-mail: luchetta@ unifi.it).S. Manetti is with the Dipartimento di Ingegneria dell'Informazione (DINFO) of the University of Florence, Via S.Marta, 3, 50139 Firenze, Italy (e-mail: stefano.manetti@ unifi.it).M.C. Piccirilli is with the Dipartimento di Ingegneria dell'Informazione (DINFO) of the University of Florence, Via S.Marta, 3, 50139 Firenze, Italy (e-mail: mariacristina.piccirilli@ unifi.it). sufficient to achieve the goal, because, in general, the supervised reference of the lumped model is not available. In order to overcome this limitation, another network must be added, having the role of approximating and "inverting" a network function of the chosen lumped model. The output of this layer consists of the numerical estim...

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“…; 0Þ T and k Á k is the Euclidean norm. Transforming sequentially each column of A yields an upper triangular matrix R: Details for the Householder QR decomposition algorithm can be found in [14]. The robust fit quality measure is given by the 'FitQuality' function whose parameters are E; p; and scale:…”

Section: Iterative Reweighted Least Squares (Irls)mentioning

confidence: 99%

Performance analysis of a novel GPU computation-to-core mapping scheme for robust facet image modeling

Park

Cao

Watson

et al. 2012

J Real-Time Image Proc

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Modern graphics processing units (GPUs) are commodity data-parallel coprocessors capable of high performance computation and data throughput. It is well known that the GPUs are ideal implementation platforms for image processing applications. However, the level of efforts and expertise to optimize the application performance is still substantial. This paper investigates the computation-to-core mapping strategies to probe the efficiency and scalability of the robust facet image modeling algorithm on GPUs. Our fine-grained computation-to-core mapping scheme achieves a significant performance gain over the standard pixel-wise mapping scheme. With indepth performance comparisons across the two different mapping schemes, we analyze the impact of the level of parallelism on the GPU computation and suggest two principles for optimizing future image processing applications on the GPU platform.

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Unitary Triangularization of a Nonsymmetric Matrix

Cited by 507 publications

References 2 publications

Numerical methods for solving linear least squares problems

Numerical methods for solving linear least squares problems

Analog system modeling based on a double modified complex valued neural network

Performance analysis of a novel GPU computation-to-core mapping scheme for robust facet image modeling

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