Estimates for the Upper and Lower Bounds on the Inverse Elements of Strictly Diagonally Dominant Periodic Adding Element Tridiagonal Matrices in Signal Processing

2011 ◽  
pp. 46-51
Author(s):  
Wenling Zhao
Keyword(s):  
Signal Processing ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Tridiagonal Matrices ◽  
Diagonally Dominant

Estimates for the Lower Bounds on the Inverse Elements of Strictly Diagonally Dominant Tridiagonal Matrices in Signal Processing

2010 ◽  
Vol 121-122 ◽  
pp. 929-933
Author(s):  
Chuan Dai Dong
Keyword(s):  
Signal Processing ◽  
Lower Bounds ◽  
Practical Applications ◽  
Tridiagonal Matrices ◽  
Diagonally Dominant

In the theory and practical applications, tridiagonal matrices play a very important role. In this paper, Motivated by the references, especially [2], we give the estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal matrices.

A Fast Algorithm for the Inverse of a Tridiagonal Period Matrices in Signal Processing

2010 ◽  
Vol 159 ◽  
pp. 469-476
Author(s):  
Xi Lian Fu
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
System Design ◽  
Lower Bounds ◽  
Nonlinear Kinetics ◽  
Computational Mathematics ◽  
Diagonally Dominant ◽  
Missile System ◽  
Economics And Biology ◽  
Bearing System

The theory and method of matrix computation, as an important tool, have much important applications such as in computational mathematics, physics, image processing and recognition, missile system design, rotor bearing system, nonlinear kinetics, economics and biology etc. In this paper, Motivated by the references, especially [2], we give the estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal period matrices.

Estimates for the Lower Bounds on the Inverse Elements of Strictly Diagonally Dominant Tridiagonal Period Matrices in Signal Processing

2010 ◽  
Vol 159 ◽  
pp. 459-463
Author(s):  
Hong Ling Fan
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
System Design ◽  
Lower Bounds ◽  
Nonlinear Kinetics ◽  
Computational Mathematics ◽  
Diagonally Dominant ◽  
Missile System ◽  
Economics And Biology ◽  
Bearing System

The theory and method of matrix computation, as an important tool, have much important applications such as in computational mathematics, physics, image processing and recognition, missile system design, rotor bearing system, nonlinear kinetics, economics and biology etc. In this paper, Motivated by the references, especially [2], we give the estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal period matrices.

scholarly journals Inequalities for the Minimum Eigenvalue of Doubly Strictly Diagonally DominantM-Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ming Xu ◽  
Suhua Li ◽  
Chaoqian Li
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Upper And Lower Bounds ◽  
Matrix Inequalities ◽  
Minimum Eigenvalue ◽  
Minimal Eigenvalue ◽  
Diagonally Dominant ◽  
Linear Differential ◽  
New Inequalities

LetAbe a doubly strictly diagonally dominantM-matrix. Inequalities on upper and lower bounds for the entries of the inverse ofAare given. And some new inequalities on the lower bound for the minimal eigenvalue ofAand the corresponding eigenvector are presented to establish an upper bound for theL1-norm of the solutionx(t)for the linear differential systemdx/dt=-Ax(t),x(0)=x0>0.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

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