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 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 Mathematical modeling of optimal product supply strategies for manufacturer-to-group customers based on semi-real demand patterns

2020 ◽  
Vol 12 ◽  
pp. 184797902094148
Author(s):  
Zhiyi Zhuo ◽  
Ka Yin Chau ◽  
Shizheng Huang ◽  
Yun Kit Ip
Keyword(s):  
Optimal Pricing ◽  
Production Volume ◽  
Demand Model ◽  
Optimal Production ◽  
Numerical Examples ◽  
The Core ◽  
Demand Pattern ◽  
Optimization Principle ◽  
Optimal Value ◽  
Demand Patterns

Customer demand is the core of the vendor’s implementation of product supply strategies. There are three different patterns of demand: real demand, false demand, and semi-real demand. For this article, we study the product supply strategy formulated for manufacturer-to-group customers based on a semi-real demand pattern. Firstly, we construct two mathematical models in which the manufacturer obtains the best profit based on the two supply modes in the semi-real demand pattern. Secondly, we solve the optimal production volume and optimal pricing. Finally, numerical examples are used to verify the validity of the model. In accordance with the optimization principle, results of the analysis are extended to the range of optimal value of product profit in the demand model, so as to explore the mechanism of manufacturers for maximizing group customers’ product profits under the semi-real demand model.

scholarly journals Infinity norm bounds for the inverse of Nekrasov matrices

2013 ◽  
Vol 219 (10) ◽  
pp. 5020-5024 ◽  
Author(s):  
Ljiljana Cvetković ◽  
Ping-Fan Dai ◽  
Ksenija Doroslovački ◽  
Yao-Tang Li
Keyword(s):  
Infinity Norm ◽  
Nekrasov Matrices

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>

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 Lower bounds to eigenvalues of the Schrödinger equation by solution of a 90-y challenge

2020 ◽  
Vol 117 (28) ◽  
pp. 16181-16186
Author(s):  
Rocco Martinazzo ◽  
Eli Pollak
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Spectral Features ◽  
Numerical Examples ◽  
Tunneling Splittings ◽  
Order Of Magnitude ◽  
Bound Theorem ◽  
Math Phys ◽  
Better Than

The Ritz upper bound to eigenvalues of Hermitian operators is essential for many applications in science. It is a staple of quantum chemistry and physics computations. The lower bound devised by Temple in 1928 [G. Temple,Proc. R. Soc. A Math. Phys. Eng. Sci.119, 276–293 (1928)] is not, since it converges too slowly. The need for a good lower-bound theorem and algorithm cannot be overstated, since an upper bound alone is not sufficient for determining differences between eigenvalues such as tunneling splittings and spectral features. In this paper, after 90 y, we derive a generalization and improvement of Temple’s lower bound. Numerical examples based on implementation of the Lanczos tridiagonalization are provided for nontrivial lattice model Hamiltonians, exemplifying convergence over a range of 13 orders of magnitude. This lower bound is typically at least one order of magnitude better than Temple’s result. Its rate of convergence is comparable to that of the Ritz upper bound. It is not limited to ground states. These results complement Ritz’s upper bound and may turn the computation of lower bounds into a staple of eigenvalue and spectral problems in physics and chemistry.

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

A Study on ARQ Policies for Data Transmission based on Kullback–Leibler Information

1998 ◽  
Vol 05 (01) ◽  
pp. 5-13
Author(s):  
Kiyoshi Sawada ◽  
Hiroaki Sandoh ◽  
Toshio Nakagawa
Keyword(s):  
Statistical Model ◽  
Upper Bound ◽  
Data Transmission ◽  
Numerical Examples ◽  
Model Based ◽  
Leibler Information

This study discusses methods for designing two types of ARQ policy; (1) the usual ARQ policy and (2) the extended ARQ policy, which is proposed in this study. In the protocol of the usual ARQ policy, the upper bound for the number of retransmissions of the data is empirically determined. A statistical model and a model based on Kullback–Leibler information (K–L model) are proposed for determining such a upper bound of retransmissions. Both the models are also applied to the extended ARQ policy. Numerical examples are presented to illustrate the K–L model which makes the design of ARQ policies easier than the statistical model.

Dual Bounds for Periodical Stochastic Programs

2022 ◽  
Author(s):  
Alexander Shapiro ◽  
Yi Cheng
Keyword(s):  
Upper Bound ◽  
Numerical Experiments ◽  
Dual Problem ◽  
Infinite Horizon ◽  
Stochastic Program ◽  
Discount Factor ◽  
Stochastic Programs ◽  
Multistage Stochastic Program ◽  
Optimal Value ◽  
Dual Bounds

A construction of the dual of a periodical formulation of infinite-horizon linear stochastic programs with a discount factor is discussed. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound, especially when the discount factor is close to one.

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