scholarly journals The Diagonally Dominant Degree and Disc Separation for the Schur Complement of Ostrowski Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Jianxing Zhao ◽  
Feng Wang ◽  
Yaotang Li
Keyword(s):  
Upper Bound ◽  
Schur Complement ◽  
Numerical Examples ◽  
Infinity Norm ◽  
Diagonally Dominant ◽  
Inequality Techniques

By applying the properties of Schur complement and some inequality techniques, some new estimates of diagonally and doubly diagonally dominant degree of the Schur complement of Ostrowski matrix are obtained, which improve the main results of Liu and Zhang (2005) and Liu et al. (2012). As an application, we present new inclusion regions for eigenvalues of the Schur complement of Ostrowski matrix. In addition, a new upper bound for the infinity norm on the inverse of the Schur complement of Ostrowski matrix is given. Finally, we give numerical examples to illustrate the theory results.

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.

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.

The Schur Complement on Weak Block Diagonally Dominant Matrices and Weak Block H-Matrices

2011 ◽  
Vol 148-149 ◽  
pp. 1523-1526
Author(s):  
Shi Hong Liu ◽  
Hong Su ◽  
Zhuo Hong Huang
Keyword(s):  
Schur Complement ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant

In this paper, we prove that the Schur complement of Weak block diagonally dominant matrices and weak block H-matrices are Weak block diagonally dominant matrices and weak block H-matrices, respectively.

scholarly journals Convergence of Relaxed Matrix Parallel Multisplitting Chaotic Methods forH-Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Li-Tao Zhang ◽  
Jian-Lei Li ◽  
Tong-Xiang Gu ◽  
Xing-Ping Liu
Keyword(s):  
Numerical Experiments ◽  
Convergence Property ◽  
Numerical Examples ◽  
Convergence Results ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant

Based on the methods presented by Song and Yuan (1994), we construct relaxed matrix parallel multisplitting chaotic generalized USAOR-style methods by introducing more relaxed parameters and analyze the convergence of our methods when coefficient matrices areH-matrices or irreducible diagonally dominant matrices. The parameters can be adjusted suitably so that the convergence property of methods can be substantially improved. Furthermore, we further study some applied convergence results of methods to be convenient for carrying out numerical experiments. Finally, we give some numerical examples, which show that our convergence results are applied and easily carried out.

Discussion for Block H-Matrices

2014 ◽  
Vol 1006-1007 ◽  
pp. 1039-1042
Author(s):  
Hui Shuang Gao
Keyword(s):  
Necessary Condition ◽  
Numerical Examples ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant ◽  
Sufficient And Necessary Condition

In this paper, a new sufficient and necessary condition for judging block strictly-double diagonally dominant matrices is given firstly. By this theorem, some new practical criteria for nonsingular blockH-matrices are obtained. In the end, the result effectiveness is illustrated by numerical examples.

scholarly journals Improving Results on Convergence of AOR Method

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Guangbin Wang ◽  
Ting Wang ◽  
Yanli Du
Keyword(s):  
Sufficient Conditions ◽  
Numerical Examples ◽  
Diagonally Dominant Matrix ◽  
Aor Method ◽  
Diagonally Dominant ◽  
Dominant Matrix

We present some sufficient conditions on convergence of AOR method for solvingAx=bwithAbeing a strictly doublyαdiagonally dominant matrix. Moreover, we give two numerical examples to show the advantage of the new results.

scholarly journals An S-type upper bound for the largest singular value of nonnegative rectangular tensors

2016 ◽  
Vol 14 (1) ◽  
pp. 925-933 ◽  
Author(s):  
Jianxing Zhao ◽  
Caili Sang
Keyword(s):  
Upper Bound ◽  
Singular Value ◽  
Numerical Examples ◽  
Rectangular Tensors ◽  
Theoretical Results

AbstractAn S-type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n} into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (2011). Numerical examples are given to verify the theoretical results.

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>

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