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 lower bound for the smallest singular value

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2711-2723
Author(s):  
Ksenija Doroslovacki ◽  
Ljiljana Cvetkovic ◽  
Ernest Sanca
Keyword(s):  
Lower Bound ◽  
Boundary Value Problems ◽  
Lower Bounds ◽  
Large Scale ◽  
Block Structure ◽  
Upper Bounds ◽  
Singular Value ◽  
Ecological Modelling ◽  
Infinity Norm ◽  
Smallest Singular Value

The aim of this paper is to obtain new lower bounds for the smallest singular value for some special subclasses of nonsingularH-matrices. This is done in two steps: first, unifying principle for deriving new upper bounds for the norm 1 of the inverse of an arbitrary nonsingular H-matrix is presented, and then, it is combined with some well-known upper bounds for the infinity norm of the inverse. The importance and efficiency of the results are illustrated by an example from ecological modelling, as well as on a type of large-scale matrices posessing a block structure, arising in boundary value problems.

scholarly journals Lower Bounds of the Smallest Singular Value of Matrices

2021 ◽  
Vol 13 (5) ◽  
pp. 1
Author(s):  
Liao Ping
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Singular Value ◽  
Euclidean Norm ◽  
Numerical Examples ◽  
Smallest Singular Value

In this paper, we get a lower bound of the smallest singular value of an arbitrarily matrix A by the trace of H(A) and the Euclidean norm of H(A), where H(A) is Hermitian part of A, numerical examples show the e ectiveness of our results.

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 Inventory Models with Defective Units and Sub-Lot Inspection

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1038
Author(s):  
Han-Wen Tuan ◽  
Gino K. Yang ◽  
Kuo-Chen Hung
Keyword(s):  
Lower Bound ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Interior Solution ◽  
Order Quantity ◽  
Inventory Models ◽  
Defective Items ◽  
Numerical Examples ◽  
Counter Example ◽  
Analytical Foundation

Inventory models must consider the probability of sub-optimal manufacturing and careless shipping to prevent the delivery of defective products to retailers. Retailers seeking to preserve a reputation of quality must also perform inspections of all items prior to sale. Inventory models that include sub-lot sampling inspections provide reasonable conditions by which to establish a lower bound and a pair of upper bounds in terms of order quantity. This should make it possible to determine the conditions of an optimal solution, which includes a unique interior solution to the problem of an order quantity satisfying the first partial derivative. The approach proposed in this paper can be used to solve the boundary. These study findings provide the analytical foundation for an inventory model that accounts for defective items and sub-lot sampling inspections. The numerical examples presented in a previous paper are used to demonstrate the derivation of an optimal solution. A counter-example is constructed to illustrate how existing iterative methods do not necessarily converge to the optimal solution.

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.

A parameterized lower bound for the smallest singular value

2008 ◽  
Vol 17 ◽  
Author(s):  
Wei Zhang ◽  
Zheng-Zhi Han ◽  
Shu-Qian Shen
Keyword(s):  
Lower Bound ◽  
Singular Value ◽  
Smallest Singular Value

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.

Sign in / Sign up

Export Citation Format

Share Document