scholarly journals Norm bounds for the inverse for generalized Nekrasov matrices in point-wise and block case

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2705-2714
Author(s):  
M. Nedovic
Keyword(s):  
Numerical Examples ◽  
Lower Semi ◽  
Nekrasov Matrices ◽  
Norm Bound

Lower-semi-Nekrasov matrices represent a generalization of Nekrasov matrices. For the inverse of lower-semi-Nekrasov matrices, a max-norm bound is proposed. Numerical examples are given to illustrate that new norm bound can give tighter results compared to already known bounds when applied to Nekrasov matrices. Also, we presented new max-norm bounds for the inverse of lower-semi-Nekrasov matrices in the block case. We considered two types of block generalizations and illustrated the results with numerical examples.

scholarly journals CKV-type $ B $-matrices and error bounds for linear complementarity problems

2021 ◽  
Vol 6 (10) ◽  
pp. 10846-10860
Author(s):  
Xinnian Song ◽  
◽  
Lei Gao
Keyword(s):  
Error Bound ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Type B ◽  
Numerical Examples ◽  
Infinity Norm ◽  
Norm Bound ◽  
Special Case ◽  
Better Than

<abstract><p>In this paper, we introduce a new subclass of $ P $-matrices called Cvetković-Kostić-Varga type $ B $-matrices (CKV-type $ B $-matrices), which contains DZ-type-$ B $-matrices as a special case, and present an infinity norm bound for the inverse of CKV-type $ B $-matrices. Based on this bound, we also give an error bound for linear complementarity problems of CKV-type $ B $-matrices. It is proved that the new error bound is better than that provided by Li et al. <sup>[<xref ref-type="bibr" rid="b24">24</xref>]</sup> for DZ-type-$ B $-matrices, and than that provided by M. García-Esnaola and J.M. Peña <sup>[<xref ref-type="bibr" rid="b10">10</xref>]</sup> for $ B $-matrices in some cases. Numerical examples demonstrate the effectiveness of the obtained results.</p></abstract>

scholarly journals Note on subdirect sums of $ \{i_0\} $-Nekrasov matrices

2021 ◽  
Vol 7 (1) ◽  
pp. 617-631
Author(s):  
Jing Xia ◽  
Keyword(s):  
Scientific Computing ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
Direct Sum ◽  
Nekrasov Matrices

<abstract><p>The concept of $ k $-subdirect sums of matrices, as a generalization of the usual sum and the direct sum, plays an important role in scientific computing. In this paper, we introduce a new subclass of $ S $-Nekrasov matrices, called $ \{i_0\} $-Nekrasov matrices, and some sufficient conditions are given which guarantee that the $ k $-subdirect sum $ A\bigoplus_k B $ is an $ \{i_0\} $-Nekrasov matrix, where $ A $ is an $ \{i_0\} $-Nekrasov matrix and $ B $ is a Nekrasov matrix. Numerical examples are reported to illustrate the conditions presented.</p></abstract>

scholarly journals Improvements on the infinity norm bound for the inverse of Nekrasov matrices

2015 ◽  
Vol 71 (3) ◽  
pp. 613-630 ◽  
Author(s):  
Chaoqian Li ◽  
Hui Pei ◽  
Aning Gao ◽  
Yaotang Li
Keyword(s):  
Infinity Norm ◽  
Nekrasov Matrices ◽  
Norm Bound

scholarly journals Generalizations of Nekrasov matrices and applications

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Ljiljana Cvetković ◽  
Vladimir Kostić ◽  
Maja Nedović
Keyword(s):  
Inverse Matrix ◽  
Index Set ◽  
Main Motivation ◽  
Numerical Examples ◽  
Nekrasov Matrices ◽  
The Given

AbstractIn this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already calculated in order to conclude that the given matrix is nonsingular. Also, we present new max-norm bounds for the inverse matrix and illustrate these results by numerical examples, comparing the results to some already known bounds for Nekrasov matrices.

scholarly journals A New Upper Bound on the Infinity Norm of the Inverse of Nekrasov Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Lei Gao ◽  
Chaoqian Li ◽  
Yaotang Li
Keyword(s):  
Upper Bound ◽  
Numerical Examples ◽  
Infinity Norm ◽  
Optimal Value ◽  
Nekrasov Matrices

A new upper bound which involves a parameter for the infinity norm of the inverse of Nekrasov matrices is given. And we determine the optimal value of the parameter such that the bound improves the results of Kolotilina, 2013. Numerical examples are given to illustrate the corresponding results.

scholarly journals Norm bounds for the inverse and error bounds for linear complementarity problems for {P1,P2}-Nekrasov matrices

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 239-250
Author(s):  
M. Nedovic ◽  
Lj. Cvetkovic
Keyword(s):  
Error Bound ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Different Types ◽  
Nekrasov Matrices

{P1,P2}-Nekrasov matrices represent a generalization of Nekrasov matrices via permutations. In this paper, we obtained an error bound for linear complementarity problems for fP1; P2g-Nekrasov matrices. Numerical examples are given to illustrate that new error bound can give tighter results compared to already known bounds when applied to Nekrasov matrices. Also, we presented new max-norm bounds for the inverse of {P1,P2}-Nekrasov matrices in the block case, considering two different types of block generalizations. Numerical examples show that new norm bounds for the block case can give tighter results compared to already known bounds for the point-wise case.

scholarly journals Schur Complement-Based Infinity Norm Bounds for the Inverse of GDSDD Matrices

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 186
Author(s):  
Yating Li ◽  
Yaqiang Wang
Keyword(s):  
Lower Bound ◽  
Schur Complement ◽  
Upper Bounds ◽  
Singular Value ◽  
Numerical Examples ◽  
Infinity Norm ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant ◽  
Norm Bound ◽  
Smallest Singular Value

Based on the Schur complement, some upper bounds for the infinity norm of the inverse of generalized doubly strictly diagonally dominant matrices are obtained. In addition, it is shown that the new bound improves the previous bounds. Numerical examples are given to illustrate our results. By using the infinity norm bound, a lower bound for the smallest singular value is given.

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

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