Construction of Lefkovitch and doubly Lefkovitch matrices with maximal eigenvalues and some diagonal elements prescribed

2021 ◽  
Author(s):  
S. Arela-Pérez ◽  
Hans Nina ◽  
Jésica Pantáz ◽  
H. Pickmann-Soto ◽  
Elvis Valero
Keyword(s):  
Maximal Eigenvalues

scholarly journals An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Gang Wang ◽  
Lihong Sun
Keyword(s):  
Efficient Algorithm ◽  
Positive Definiteness ◽  
Numerical Results ◽  
Nonnegative Matrices ◽  
Maximal Eigenvalue ◽  
Positive Semidefiniteness ◽  
Maximal Eigenvalues ◽  
Modified Algorithm

In this paper, we propose an improved power algorithm for finding maximal eigenvalues. Without any partition, we can get the maximal eigenvalue and show that the modified power algorithm is convergent for zero symmetric reducible nonnegative matrices. Numerical results are reported to demonstrate the effectiveness of the modified power algorithm. Finally, a modified algorithm is proposed to test the positive definiteness (positive semidefiniteness) of Z-matrices.

scholarly journals Extreme Spectra Realization by Nonsymmetric Tridiagonal and Nonsymmetric Arrow Matrices

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
H. Pickmann-Soto ◽  
S. Arela-Pérez ◽  
Juan C. Egaña ◽  
Ricardo L. Soto
Keyword(s):  
Sufficient Conditions ◽  
Real Vector ◽  
The Real ◽  
Extreme Eigenvalue ◽  
The Matrix ◽  
Maximal Eigenvalues ◽  
Principal Submatrices ◽  
Solution Matrix ◽  
Arrow Matrix ◽  
Algorithmic Procedure

We consider the following inverse extreme eigenvalue problem: given the real numbers {λ1j,λjj}j=1n and the real vector x(n)=x1,x2,…,xn, to construct a nonsymmetric tridiagonal matrix and a nonsymmetric arrow matrix such that {λ1j,λjj}j=1n are the minimal and the maximal eigenvalues of each one of their leading principal submatrices, and x(n),λn(n) is an eigenpair of the matrix. We give sufficient conditions for the existence of such matrices. Moreover our results generate an algorithmic procedure to compute a unique solution matrix.

scholarly journals The Applicability of Bipartite Graph Model for Thunderstorms Forecast over Kolkata

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Sutapa Chaudhuri ◽  
Anirban Middey
Keyword(s):  
Relative Humidity ◽  
Bipartite Graph ◽  
Convective Available Potential Energy ◽  
Graph Model ◽  
India Meteorological Department ◽  
Graph Connectivity ◽  
Threshold Values ◽  
Single Spectrum ◽  
Eigen Values ◽  
Maximal Eigenvalues

Single Spectrum Bipartite Graph (SSBG) model is developed to forecast thunderstorms over Kolkata(22∘32′N,88∘20′E)during the premonsoon season (April-May). The statistical distribution of normal probability is observed for temperature, relative humidity, convective available potential energy (CAPE), and convective inhibition energy (CIN) to quantify the threshold values of the parameters for the prevalence of thunderstorms. Method of conditional probability is implemented to ascertain the possibilities of the occurrence of thunderstorms within the ranges of the threshold values. The single spectrum bipartite graph connectivity model developed in this study consists of two sets of vertices; one set includes two time vertices (00UTC, 12UTC) and the other includes four meteorological parameters: temperature, relative humidity, CAPE, and CIN. Three distinct ranges of maximal eigen values are obtained for the three categories of thunderstorms. Maximal eigenvalues for severe, ordinary, and no thunderstorm events are observed to be(2.6±0.12),(1.88±0.09), and(1.26±.03), respectively. The ranges of the threshold values obtained using ten year data (1997–2006) are considered as the reference range and the result is validated with the IMD (India Meteorological Department) observation, Doppler Weather Radar (DWR) Products, and satellite images of 2007. The result reveals that the model provides 12- to 6-hour forecast (nowcasting) of thunderstorms with 96% to 98% accuracy.

scholarly journals Algebraic flux correction schemes preserving the eigenvalue range of symmetric tensor fields

2019 ◽  
Vol 53 (3) ◽  
pp. 833-867 ◽  
Author(s):  
Christoph Lohmann
Keyword(s):  
Galerkin Approximation ◽  
Symmetric Tensor ◽  
Stationary Solutions ◽  
Maximum Principles ◽  
Tensor Fields ◽  
Flux Correction ◽  
Diffusion Operator ◽  
Continuous Galerkin ◽  
Maximal Eigenvalues ◽  
Edge Based

This work extends the algebraic flux correction (AFC) paradigm to finite element discretizations of conservation laws for symmetric tensor fields. The proposed algorithms are designed to enforce discrete maximum principles and preserve the eigenvalue range of evolving tensors. To that end, a continuous Galerkin approximation is modified by adding a linear artificial diffusion operator and a nonlinear antidiffusive correction. The latter is decomposed into edge-based fluxes and constrained to prevent violations of local bounds for the minimal and maximal eigenvalues. In contrast to the flux-corrected transport (FCT) algorithm developed previously by the author and existing slope limiting techniques for stress tensors, the admissible eigenvalue range is defined implicitly and the limited antidiffusive terms are incorporated into the residual of the nonlinear system. In addition to scalar limiters that use a common correction factor for all components of a tensor-valued antidiffusive flux, tensor limiters are designed using spectral decompositions. The new limiter functions are analyzed using tensorial extensions of the existing AFC theory for scalar convection-diffusion equations. The proposed methodology is backed by rigorous proofs of eigenvalue range preservation and Lipschitz continuity. Convergence of pseudo time-stepping methods to stationary solutions is demonstrated in numerical studies.

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