**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**975

# Search results for: Kraljic’s matrix

##### 975 On Generalized New Class of Matrix Polynomial Set

**Authors:**
Ghazi S. Kahmmash

**Abstract:**

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

**Keywords:**
Generating functions,
Recurrences relation and Generalization of the new class matrix polynomial set.

##### 974 Selection of Strategic Suppliers for Partnership: A Model with Two Stages Approach

**Authors:**
Safak Isik,
Ozalp Vayvay

**Abstract:**

Strategic partnerships with suppliers play a vital role for the long-term value-based supply chain. This strategic collaboration keeps still being one of the top priority of many business organizations in order to create more additional value; benefiting mainly from supplier’s specialization, capacity and innovative power, securing supply and better managing costs and quality. However, many organizations encounter difficulties in initiating, developing and managing those partnerships and many attempts result in failures. One of the reasons for such failure is the incompatibility of members of this partnership or in other words wrong supplier selection which emphasize the significance of the selection process since it is the beginning stage. An effective selection process of strategic suppliers is critical to the success of the partnership. Although there are several research studies to select the suppliers in literature, only a few of them is related to strategic supplier selection for long-term partnership. The purpose of this study is to propose a conceptual model for the selection of strategic partnership suppliers. A two-stage approach has been used in proposed model incorporating first segmentation and second selection. In the first stage; considering the fact that not all suppliers are strategically equal and instead of a long list of potential suppliers, Kraljic’s purchasing portfolio matrix can be used for segmentation. This supplier segmentation is the process of categorizing suppliers based on a defined set of criteria in order to identify types of suppliers and determine potential suppliers for strategic partnership. In the second stage, from a pool of potential suppliers defined at first phase, a comprehensive evaluation and selection can be performed to finally define strategic suppliers considering various tangible and intangible criteria. Since a long-term relationship with strategic suppliers is anticipated, criteria should consider both current and future status of the supplier. Based on an extensive literature review; strategical, operational and organizational criteria have been determined and elaborated. The result of the selection can also be used to determine suppliers who are not ready for a partnership but to be developed for strategic partnership. Since the model is based on multiple criteria for both stages, it provides a framework for further utilization of Multi-Criteria Decision Making (MCDM) techniques. The model may also be applied to a wide range of industries and involve managerial features in business organizations.

**Keywords:**
Kraljic’s matrix,
purchasing portfolio,
strategic supplier selection,
supplier collaboration,
supplier partnership,
supplier segmentation.

##### 973 The Partial Non-combinatorially Symmetric N10 -Matrix Completion Problem

**Authors:**
Gu-Fang Mou,
Ting-Zhu Huang

**Abstract:**

An n×n matrix is called an N1 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N1 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N1 0 -completion. Therefore, we have given sufficient conditions that guarantee the existence of the N1 0 -completion for these digraphs.

**Keywords:**
Matrix completion,
matrix completion,
N10 -matrix,
non-combinatorially symmetric,
cycle,
digraph.

##### 972 Fuzzy Adjacency Matrix in Graphs

**Authors:**
Mahdi Taheri,
Mehrana Niroumand

**Abstract:**

**Keywords:**
Graph,
adjacency matrix,
fuzzy numbers

##### 971 Inverse Matrix in the Theory of Dynamic Systems

**Authors:**
R. Masarova,
M. Juhas,
B. Juhasova,
Z. Sutova

**Abstract:**

**Keywords:**
Dynamic system,
transfer matrix,
inverse matrix,
modeling.

##### 970 Numerical Treatment of Matrix Differential Models Using Matrix Splines

**Authors:**
Kholod M. Abualnaja

**Abstract:**

This paper consider the solution of the matrix differential models using quadratic, cubic, quartic, and quintic splines. Also using the Taylor’s and Picard’s matrix methods, one illustrative example is included.

**Keywords:**
Matrix Splines,
Cubic Splines,
Quartic Splines.

##### 969 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices

**Authors:**
Zhuan-de Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

**Keywords:**
Backward MPSD iterative matrix,
Jacobi iterative matrix,
eigenvalue,
p-cyclic matrix.

##### 968 On Positive Definite Solutions of Quaternionic Matrix Equations

**Authors:**
Minghui Wang

**Abstract:**

**Keywords:**
Matrix equation,
Quaternionic matrix,
Real representation,
positive (semi)definite solutions.

##### 967 Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network

**Authors:**
Won Sup Kim,
Xue-Mei Cui,
Seung Kee Han

**Abstract:**

We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.

**Keywords:**
Chaotic oscillator,
complex network,
inverse coherence matrix,
network estimation.

##### 966 Solving Linear Matrix Equations by Matrix Decompositions

**Authors:**
Yongxin Yuan,
Kezheng Zuo

**Abstract:**

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

**Keywords:**
Matrix equation,
Generalized inverse,
Generalized
singular-value decomposition.

##### 965 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices

**Authors:**
Zuan-De Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

**Keywords:**
Backward USSOR iterative matrix,
Jacobi iterative matrix,
convergence,
spectral radius

##### 964 An Algorithm of Ordered Schur Factorization For Real Nonsymmetric Matrix

**Authors:**
Lokendra K. Balyan

**Abstract:**

**Keywords:**
Schur Factorization,
Eigenvalues of nonsymmetric matrix,
Orthoganal matrix.

##### 963 Tree Sign Patterns of Small Order that Allow an Eventually Positive Matrix

**Authors:**
Ber-Lin Yu,
Jie Cui,
Hong Cheng,
Zhengfeng Yu

**Abstract:**

**Keywords:**
Eventually positive matrix,
sign pattern,
tree.

##### 962 Numerical Simulation of Effect of Various Rib Configurations on Enhancing Heat Transfer of Matrix Cooling Channel

**Authors:**
Seok Min Choi,
Minho Bang,
Seuong Yun Kim,
Hyungmin Lee,
Won-Gu Joo,
Hyung Hee Cho

**Abstract:**

**Keywords:**
Matrix cooling,
rib,
heat transfer,
gas turbine.

##### 961 Bounds on the Second Stage Spectral Radius of Graphs

**Authors:**
S.K.Ayyaswamy,
S.Balachandran,
K.Kannan

**Abstract:**

Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.

**Keywords:**
Second stage spectral radius,
Irreducible matrix,
Derived graph

##### 960 Some New Subclasses of Nonsingular H-matrices

**Authors:**
Guangbin Wang,
Liangliang Li,
Fuping Tan

**Abstract:**

In this paper, we obtain some new subclasses of non¬singular H-matrices by using a diagonally dominant matrix

**Keywords:**
H-matrix,
diagonal dominance,
a diagonally dominant matrix.

##### 959 Redundancy Component Matrix and Structural Robustness

**Authors:**
Xinjian Kou,
Linlin Li,
Yongju Zhou,
Jimian Song

**Abstract:**

We introduce the redundancy matrix that expresses clearly the geometrical/topological configuration of the structure. With the matrix, the redundancy of the structure is resolved into redundant components and assigned to each member or rigid joint. The values of the diagonal elements in the matrix indicates the importance of the corresponding members or rigid joints, and the geometrically correlations can be shown with the non-diagonal elements. If a member or rigid joint failures, reassignment of the redundant components can be calculated with the recursive method given in the paper. By combining the indexes of reliability and redundancy components, we define an index concerning the structural robustness. To further explain the properties of the redundancy matrix, we cited several examples of statically indeterminate structures, including two trusses and a rigid frame. With the examples, some simple results and the properties of the matrix are discussed. The examples also illustrate that the redundancy matrix and the relevant concepts are valuable in structural safety analysis.

**Keywords:**
Structural robustness,
structural reliability,
redundancy component,
redundancy matrix.

##### 958 Newton-Raphson State Estimation Solution Employing Systematically Constructed Jacobian Matrix

**Authors:**
Nursyarizal Mohd Nor,
Ramiah Jegatheesan,
Perumal Nallagownden

**Abstract:**

**Keywords:**
State Estimation (SE),
Weight Least Square (WLS),
Newton-Raphson State Estimation (NRSE),
Jacobian matrix H.

##### 957 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

*AXB=C*and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

**Keywords:**
Iterative method,
symmetric arrowhead matrix,
conjugate gradient algorithm.

##### 956 Membership Surface and Arithmetic Operations of Imprecise Matrix

**Authors:**
Dhruba Das

**Abstract:**

**Keywords:**
Imprecise number,
Imprecise vector,
Membership
surface,
Imprecise matrix.

##### 955 On the Positive Definite Solutions of Nonlinear Matrix Equation

**Authors:**
Tian Baoguang,
Liang Chunyan,
Chen Nan

**Abstract:**

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_{i} are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_{i}<0 is proposed.

**Keywords:**
Nonlinear matrix equation,
Positive definite solution,
The maximal-minimal solution,
Iterative method,
Free-inversion

##### 954 An Iterative Method for the Symmetric Arrowhead Solution of Matrix Equation

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

**Keywords:**
Symmetric arrowhead matrix,
iterative method,
like-minimum norm,
minimum norm,
Algorithm LSQR.

##### 953 Spectroscopic and SEM Investigation of TCPP in Titanium Matrix

**Authors:**
R.Rahimi,
F.Moharrami

**Abstract:**

Titanium gels doped with water-soluble cationic porphyrin were synthesized by the sol–gel polymerization of Ti (OC4H9)4. In this work we investigate the spectroscopic properties along with SEM images of tetra carboxyl phenyl porphyrin when incorporated into porous matrix produced by the sol–gel technique.

**Keywords:**
TCPP,
Titanium matrix,
UV/Vis spectroscopy,
SEM.

##### 952 Two Iterative Algorithms to Compute the Bisymmetric Solution of the Matrix Equation A1X1B1 + A2X2B2 + ... + AlXlBl = C

**Authors:**
A.Tajaddini

**Abstract:**

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

**Keywords:**
Bisymmetric matrices,
Paige’s algorithms,
Least
square.

##### 951 Iterative solutions to the linear matrix equation AXB + CXTD = E

**Authors:**
Yongxin Yuan,
Jiashang Jiang

**Abstract:**

**Keywords:**
matrix equation,
iterative algorithm,
parameter estimation,
minimum norm solution.

##### 950 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning

**Authors:**
Azita Tajaddini,
Ramleh Shamsi

**Abstract:**

**Keywords:**
Linear matrix equation,
Block GMRES,
matrix Krylov
subspace,
polynomial preconditioner.

##### 949 Image Sensor Matrix High Speed Simulation

**Authors:**
Z. Feng,
V. Viswanathan,
D. Navarro,
I. O'Connor

**Abstract:**

This paper presents a new high speed simulation methodology to solve the long simulation time problem of CMOS image sensor matrix. Generally, for integrating the pixel matrix in SOC and simulating the system performance, designers try to model the pixel in various modeling languages such as VHDL-AMS, SystemC or Matlab. We introduce a new alternative method based on spice model in cadence design platform to achieve accuracy and reduce simulation time. The simulation results indicate that the pixel output voltage maximum error is at 0.7812% and time consumption reduces from 2.2 days to 13 minutes achieving about 240X speed-up for the 256x256 pixel matrix.

**Keywords:**
CMOS image sensor,
high speed simulation,
image
sensor matrix simulation.

##### 948 Sign Pattern Matrices that Admit P0 Matrices

**Authors:**
Ling Zhang,
Ting-Zhu Huang

**Abstract:**

A P0-matrix is a real square matrix all of whose principle minors are nonnegative. In this paper, we consider the class of P0-matrix. Our main aim is to determine which sign pattern matrices are admissible for this class of real matrices.

**Keywords:**
Sign pattern matrices,
P0 matrices,
graph,
digraph.

##### 947 The Inverse Eigenvalue Problem via Orthogonal Matrices

**Authors:**
A. M. Nazari,
B. Sepehrian,
M. Jabari

**Abstract:**

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

**Keywords:**
Householder matrix,
nonnegative matrix,
Inverse eigenvalue problem.

##### 946 A Constitutive Model of Ligaments and Tendons Accounting for Fiber-Matrix Interaction

**Authors:**
Ratchada Sopakayang,
Gerhard A. Holzapfel

**Abstract:**

**Keywords:**
Hyperelasticity,
constitutive model,
fiber-matrix
interaction,
ligament,
tendon.