scholarly journals Extensions of pseudo-Perron-Frobenius splitting related to generalized inverse AT,S(2)

2018 ◽  
Vol 6 (1) ◽  
pp. 46-55
Author(s):  
Shaowu Huang ◽  
Qing-Wen Wang ◽  
Shuxia Wu ◽  
Yaoming Yu
Keyword(s):  
Generalized Inverse ◽  
Multilinear Algebra ◽  
Frobenius Splitting

Abstract We in this paper define the outer-Perron-Frobenius splitting, which is an extension of the pseudo- Perron-Frobenius splitting defined in [A.N. Sushama, K. Premakumari, K.C. Sivakumar, Extensions of Perron-Frobenius splittings and relationships with nonnegative Moore-Penrose inverse, Linear and Multilinear Algebra 63 (2015) 1-11]. We present some criteria for the convergence of the outer-Perron-Frobenius splitting. The findings of this paper generalize some known results in the literatures.

scholarly journals On a conjecture of Pappas and Rapoport about the standard local model for GL_d

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinakar Muthiah ◽  
Alex Weekes ◽  
Oded Yacobi
Keyword(s):  
Type A ◽  
Positive Answer ◽  
Local Model ◽  
Schubert Varieties ◽  
Shimura Varieties ◽  
Local Models ◽  
Full Generality ◽  
Frobenius Splitting ◽  
Affine Grassmannians ◽  
Main Ideas

AbstractIn their study of local models of Shimura varieties for totally ramified extensions, Pappas and Rapoport posed a conjecture about the reducedness of a certain subscheme of {n\times n} matrices. We give a positive answer to their conjecture in full generality. Our main ideas follow naturally from two of our previous works. The first is our proof of a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman on the equations defining type A affine Grassmannians. The second is the work of the first two authors and Kamnitzer on affine Grassmannian slices and their reduced scheme structure. We also present a version of our argument that is almost completely elementary: the only non-elementary ingredient is the Frobenius splitting of Schubert varieties.

Erratum: Generalized Inverse of a Matrix Product

SIAM Review ◽  
1967 ◽  
Vol 9 (2) ◽  
pp. 249-249 ◽  
Author(s):  
T. N. E. Greville
Keyword(s):  
Generalized Inverse ◽  
Matrix Product

scholarly journals Acoustic source localization using the open spherical microphone array in the low-frequency range

2019 ◽  
Vol 283 ◽  
pp. 04001
Author(s):  
Boquan Yang ◽  
Shengguo Shi ◽  
Desen Yang
Keyword(s):  
Source Localization ◽  
Generalized Inverse ◽  
Microphone Array ◽  
Low Frequency ◽  
Poor Performance ◽  
Microphone Arrays ◽  
Three Dimension ◽  
Frequency Range ◽  
Array Aperture ◽  
Regularization Matrix

Recently, spherical microphone arrays (SMA) have become increasingly significant for source localization and identification in three dimension due to its spherical symmetry. However, conventional Spherical Harmonic Beamforming (SHB) based on SMA has limitations, such as poor resolution and high side-lobe levels in image maps. To overcome these limitations, this paper employs the iterative generalized inverse beamforming algorithm with a virtual extrapolated open spherical microphone array. The sidelobes can be suppressed and the main-lobe can be narrowed by introducing the two iteration processes into the generalized inverse beamforming (GIB) algorithm. The instability caused by uncertainties in actual measurements, such as measurement noise and configuration problems in the process of GIB, can be minimized by iteratively redefining the form of regularization matrix and the corresponding GIB localization results. In addition, the poor performance of microphone arrays in the low-frequency range due to the array aperture can be improved by using a virtual extrapolated open spherical array (EA), which has a larger array aperture. The virtual array is obtained by a kind of data preprocessing method through the regularization matrix algorithm. Both results from simulations and experiments show the feasibility and accuracy of the method.

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