The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Jianzhou Liu - One of the best experts on this subject based on the ideXlab platform.
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Authors' Reply to “Comments on `A New Trace Bound for a General Square Matrix Product' ”
IEEE Transactions on Automatic Control, 2008Co-Authors: Jianzhou LiuAbstract:We thank Prof. Robert Schmid for comments on our paper "a new trace bound for a general Square Matrix product." After thorough thought, we also think theorem 2 of the paper "a new trace bound for a general Square Matrix product" has no good practical value. We want to clarify that in our paper, we mainly improve the recent results about the trace bounds for the product of two arbitrary real Square matrices. Therefore, the title and abstract of our paper do not explicitly refer to Riccati equations. Hence, theorem 2 is only a simple application of the estimated trace bounds.
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a new trace bound for a general Square Matrix product
IEEE Transactions on Automatic Control, 2007Co-Authors: Jianzhou LiuAbstract:Using the correlated properties between the diagonal element and the singular value of the Matrix, we propose new trace bounds for the product of two arbitrary real Square matrices and improve the recent results
Mauricio D Sacchi - One of the best experts on this subject based on the ideXlab platform.
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five dimensional seismic reconstruction using parallel Square Matrix factorization
IEEE Transactions on Geoscience and Remote Sensing, 2017Co-Authors: Jianjun Gao, Jinkun Cheng, Mauricio D SacchiAbstract:Seismic data acquired by geophones are processed to estimate images of the earth’s interior that are used to explore, develop, and monitor resources and to study the shallow structure of the crust for geological, environmental, and geotechnical purposes. These multidimensional data sets are often irregularly sampled and incomplete in the so-called midpoint and offset acquisition coordinates. Multidimensional seismic data reconstruction can be viewed as a low-rank Matrix or tensor completion problem. In this paper, we introduce a fast and efficient low-rank tensor completion algorithm named parallel Square Matrix factorization (PSMF) and adopt it to reconstruct seismic data in the typical seismic data processing coordinates: frequency, midpoint, and offset. For each frequency slice, we establish a tensor minimization model composed of a low-rank constrained term and a data misfit term. Then we adopt the PSMF algorithm for the recovery of the missing samples. In the PSMF method, we avoid using unbalanced “long strip” matrices that result from conventional tensor unfolding. Instead, the tensor is unfolded into almost Square or Square matrices that are low rank. We also compare the proposed PSMF method with other completion methods. Experiments via synthetic data and field data sets validate the effectiveness of the proposed algorithm.
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a new 5d seismic reconstruction method based on a parallel Square Matrix factorization algorithm
Seg Technical Program Expanded Abstracts, 2015Co-Authors: Jianjun Gao, Jinkun Cheng, Mauricio D SacchiAbstract:Multidimensional seismic data reconstruction can be viewed as a low rank Matrix or tensor completion problem. Different rank-reduction approaches can be employed to perform seismic data interpolation and denoising. For these methods, the computational cost and reconstruction quality are two important aspects that must be carefully considered. In this paper, we present a new fast and economic tensor completion method named Parallel Square Matrix Factorization (PSMF). We apply the algorithm to the ubiquitous 5D seismic data regularization problem. 5D reconstruction entails reconstructing a series 4th-order multilinear arrays (tensors) in the frequency domain. For this purpose we transform the data to the frequency domain and 4D spatial volumes in midpoint-offset are reshaped into matrices. Rank-reduction of these matrices is at the core of our reconstruction algorithms. We show that properly reshaping the data tensor into almost Square matrices lead to an improved tensor completion algorithm. We demonstrate the effectiveness of the proposed approach via synthetic examples and by a data set from Western Canadian Sedimentary Basin.
Qiyi Wang - One of the best experts on this subject based on the ideXlab platform.
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a trace bound for a general Square Matrix product
IEEE Transactions on Automatic Control, 2000Co-Authors: Wei Xing, Qingling Zhang, Qiyi WangAbstract:Estimates of bounds on the solutions of Lyapunov and Riccati equations are important for analysis and synthesis of linear systems. In this paper, we propose new trace bounds for the product of two general matrices. The key point for removing the restriction of symmetry is to replace eigenvalues partly by singular values in the equation of bounds. The results obtained are valid for both symmetric and nonsymmetric cases and give tighter bounds in certain cases.
Jianjun Gao - One of the best experts on this subject based on the ideXlab platform.
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five dimensional seismic reconstruction using parallel Square Matrix factorization
IEEE Transactions on Geoscience and Remote Sensing, 2017Co-Authors: Jianjun Gao, Jinkun Cheng, Mauricio D SacchiAbstract:Seismic data acquired by geophones are processed to estimate images of the earth’s interior that are used to explore, develop, and monitor resources and to study the shallow structure of the crust for geological, environmental, and geotechnical purposes. These multidimensional data sets are often irregularly sampled and incomplete in the so-called midpoint and offset acquisition coordinates. Multidimensional seismic data reconstruction can be viewed as a low-rank Matrix or tensor completion problem. In this paper, we introduce a fast and efficient low-rank tensor completion algorithm named parallel Square Matrix factorization (PSMF) and adopt it to reconstruct seismic data in the typical seismic data processing coordinates: frequency, midpoint, and offset. For each frequency slice, we establish a tensor minimization model composed of a low-rank constrained term and a data misfit term. Then we adopt the PSMF algorithm for the recovery of the missing samples. In the PSMF method, we avoid using unbalanced “long strip” matrices that result from conventional tensor unfolding. Instead, the tensor is unfolded into almost Square or Square matrices that are low rank. We also compare the proposed PSMF method with other completion methods. Experiments via synthetic data and field data sets validate the effectiveness of the proposed algorithm.
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a new 5d seismic reconstruction method based on a parallel Square Matrix factorization algorithm
Seg Technical Program Expanded Abstracts, 2015Co-Authors: Jianjun Gao, Jinkun Cheng, Mauricio D SacchiAbstract:Multidimensional seismic data reconstruction can be viewed as a low rank Matrix or tensor completion problem. Different rank-reduction approaches can be employed to perform seismic data interpolation and denoising. For these methods, the computational cost and reconstruction quality are two important aspects that must be carefully considered. In this paper, we present a new fast and economic tensor completion method named Parallel Square Matrix Factorization (PSMF). We apply the algorithm to the ubiquitous 5D seismic data regularization problem. 5D reconstruction entails reconstructing a series 4th-order multilinear arrays (tensors) in the frequency domain. For this purpose we transform the data to the frequency domain and 4D spatial volumes in midpoint-offset are reshaped into matrices. Rank-reduction of these matrices is at the core of our reconstruction algorithms. We show that properly reshaping the data tensor into almost Square matrices lead to an improved tensor completion algorithm. We demonstrate the effectiveness of the proposed approach via synthetic examples and by a data set from Western Canadian Sedimentary Basin.
K. Vasudevan - One of the best experts on this subject based on the ideXlab platform.
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Stability of Two-Dimensional Systems Using Single Square Matrix
Advances in Power Systems and Energy Management, 2017Co-Authors: P. Ramesh, K. VasudevanAbstract:This article presents a new and easy unified way to investigate the stability of 2-D linear systems. The 2-D characteristics equation is regenerate into a similar one-dimensional characteristic polynomial. Using the coefficient of the equal one-dimensional characteristic polynomial, a new technique had proposed to create a single Square Matrix to check the sufficient conditions for stability analysis. To determine the stability Square Matrix should have the positive inner wise for all determinants starting from the middle elements and continuing outward up to the integrated Matrix are positive. The illustrative examples prove the simplicity and application of the suggested method.
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Multidimensional Linear Discrete System Stability Analysis Using Single Square Matrix
Advances in Power Systems and Energy Management, 2017Co-Authors: P. Ramesh, K. VasudevanAbstract:This paper reviews to search out the stability of multidimensional linear time invariant discrete system; the system, which is portrayed within the forms of the individual characteristic equation. Besides an equivalent one-dimensional equation is created from the multidimensional characteristic equation, a replacement method has planned for construction single Square Matrix using the coefficient of equivalent one-dimensional characteristic equation and determinants were evaluated using Jury’s idea. The proposed procedure for construction of single Square Matrix is compared to Jury’s Matrix formation that is incredibly simple and direct and consumes less arithmetic operations. This approach is delineated utilizing numerous numerical illustrations.
