**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3344

# Search results for: minimum norm solution.

##### 3344 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.

##### 3343 An Iterative Method for the Least-squares Symmetric Solution of AXB+CYD=F and its Application

**Authors:**
Minghui Wang

**Abstract:**

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

**Keywords:**
Matrix equation,
bisymmetric matrix,
least squares problem,
like-minimum norm,
iterative algorithm.

##### 3342 Iterative Solutions to Some Linear Matrix Equations

**Authors:**
Jiashang Jiang,
Hao Liu,
Yongxin Yuan

**Abstract:**

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

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

##### 3341 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.

##### 3340 Performance Evaluation of Music and Minimum Norm Eigenvector Algorithms in Resolving Noisy Multiexponential Signals

**Authors:**
Abdussamad U. Jibia,
Momoh-Jimoh E. Salami

**Abstract:**

Eigenvector methods are gaining increasing acceptance in the area of spectrum estimation. This paper presents a successful attempt at testing and evaluating the performance of two of the most popular types of subspace techniques in determining the parameters of multiexponential signals with real decay constants buried in noise. In particular, MUSIC (Multiple Signal Classification) and minimum-norm techniques are examined. It is shown that these methods perform almost equally well on multiexponential signals with MUSIC displaying better defined peaks.

**Keywords:**
Eigenvector,
minimum norm,
multiexponential,
subspace.

##### 3339 Combining Minimum Energy and Minimum Direct Jerk of Linear Dynamic Systems

**Authors:**
V. Tawiwat,
P. Jumnong

**Abstract:**

**Keywords:**
Optimization,
Dynamic,
Linear Systems,
Jerks.

##### 3338 An Iterative Updating Method for Damped Gyroscopic Systems

**Authors:**
Yongxin Yuan

**Abstract:**

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p<n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ¯2j−1 ∈ C, x2j = ¯x2j−1 ∈ Cn for j = 1, ··· , l, and λk ∈ R, xk ∈ Rn for k = 2l + 1, ··· , p, find real-valued symmetric matrices D,K and a real-valued skew-symmetric matrix G (that is, GT = −G) such that MaXΛ2 + (D + G)XΛ + KX = 0. Problem II: Given real-valued symmetric matrices Da, Ka ∈ Rn×n and a real-valued skew-symmetric matrix Ga, find (D, ˆ G, ˆ Kˆ ) ∈ SE such that Dˆ −Da2+Gˆ−Ga2+Kˆ −Ka2 = min(D,G,K)∈SE (D− Da2 + G − Ga2 + K − Ka2), where SE is the solution set of Problem I and · is the Frobenius norm. This paper presents an iterative algorithm to solve Problem I and Problem II. By using the proposed iterative method, a solution of Problem I can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum Frobenius norm solution of Problem I can be obtained by choosing a special kind of initial matrices. Moreover, the optimal approximation solution (D, ˆ G, ˆ Kˆ ) of Problem II can be obtained by finding the minimum Frobenius norm solution of a changed Problem I. A numerical example shows that the introduced iterative algorithm is quite efficient.

**Keywords:**
Model updating,
iterative algorithm,
gyroscopic system,
partially prescribed spectral data,
optimal approximation.

##### 3337 Application of l1-Norm Minimization Technique to Image Retrieval

**Authors:**
C. S. Sastry,
Saurabh Jain,
Ashish Mishra

**Abstract:**

Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

**Keywords:**
l1-norm minimization,
content based retrieval,
modified Gabor function.

##### 3336 Impulsive Noise-Resilient Subband Adaptive Filter

**Authors:**
Young-Seok Choi

**Abstract:**

**Keywords:**
Subband adaptive filter,
L1-norm,
system
identification,
robustness,
impulsive interference.

##### 3335 Comparison between Minimum Direct and Indirect Jerks of Linear Dynamic Systems

**Authors:**
Tawiwat Veeraklaew,
Nathasit Phathana-im,
Songkit Heama

**Abstract:**

**Keywords:**
Optimization,
Dynamic,
Linear Systems,
Jerks.

##### 3334 Subband Adaptive Filter Exploiting Sparsity of System

**Authors:**
Young-Seok Choi

**Abstract:**

**Keywords:**
Subband adaptive filtering,
sparsity constraint,
weighted l1-norm.

##### 3333 Probability of Globality

**Authors:**
Eva Eggeling,
Dieter W. Fellner,
Torsten Ullrich

**Abstract:**

**Keywords:**
global optimization,
probability theory,
probability of
globality

##### 3332 Sparsity-Aware and Noise-Robust Subband Adaptive Filter

**Authors:**
Young-Seok Choi

**Abstract:**

**Keywords:**
Subband adaptive filter,
l0-norm,
sparse system,
robustness,
impulsive interference.

##### 3331 The Ratios between the Spectral Norm, the Numerical Radius and the Spectral Radius

**Authors:**
Kui Du

**Abstract:**

Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions.

**Keywords:**
Spectral norm,
Numerical radius,
Spectral radius,
Ratios

##### 3330 A Simple Adaptive Algorithm for Norm-Constrained Optimization

**Authors:**
Hyun-Chool Shin

**Abstract:**

**Keywords:**
constrained optimization,
unit-norm,
LMS,
principle
component analysis.

##### 3329 An Efficient Iterative Updating Method for Damped Structural Systems

**Authors:**
Jiashang Jiang

**Abstract:**

Model updating is an inverse eigenvalue problem which concerns the modification of an existing but inaccurate model with measured modal data. In this paper, an efficient gradient based iterative method for updating the mass, damping and stiffness matrices simultaneously using a few of complex measured modal data is developed. Convergence analysis indicates that the iterative solutions always converge to the unique minimum Frobenius norm symmetric solution of the model updating problem by choosing a special kind of initial matrices.

**Keywords:**
Model updating,
iterative algorithm,
damped structural
system,
optimal approximation.

##### 3328 Thermodynamic Study for Aggregation Behavior of Hydrotropic Solution

**Authors:**
Meghal Desai,
Jigisha Parikh

**Abstract:**

Aggregation behavior of sodium salicylate and sodium cumene sulfonate was studied in aqueous solution at different temperature. Specific conductivity and relative viscosity were measured at different temperature to find minimum hydrotropic concentration. The thermodynamic parameters (free energy, enthalpy and entropy) were evaluated in the temperature range of 30°C-70°C. The free energy decreased with increase in temperature. The aggregation was found to be exothermic in nature and favored by positive value of entropy.

**Keywords:**
Hydrotropes,
Enthalpy,
Entropy,
Free Energy,
Minimum Hydrotropic Concentration.

##### 3327 Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic Boundary Value Problem −Δu = f(u)

**Authors:**
Abida Harbi

**Abstract:**

**Keywords:**
Error estimates,
Finite elements,
Nonlinear PDEs,
Schwarz method.

##### 3326 Minimum Energy of a Prismatic Joint with out: Actuator: Application on RRP Robot

**Authors:**
Tawiwat V.,
Tosapolporn P.,
Kedit J.

**Abstract:**

This research proposes the state of art on how to control or find the trajectory paths of the RRP robot when the prismatic joint is malfunction. According to this situation, the minimum energy of the dynamic optimization is applied. The RRP robot or similar systems have been used in many areas such as fire fighter truck, laboratory equipment and military truck for example a rocket launcher. In order to keep on task that assigned, the trajectory paths must be computed. Here, the open loop control is applied and the result of an example show the reasonable solution which can be applied to the controllable system.

**Keywords:**
RRP robot,
Optimal Control,
Minimum Energy and Under Actuator.

##### 3325 Septic B-spline Collocation Method for Solving One-dimensional Hyperbolic Telegraph Equation

**Authors:**
Marzieh Dosti,
Alireza Nazemi

**Abstract:**

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

**Keywords:**
B-spline,
collocation method,
second-order hyperbolic telegraph equation,
difference schemes.

##### 3324 Existence of Solution for Boundary Value Problems of Differential Equations with Delay

**Authors:**
Xiguang Li

**Abstract:**

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

**Keywords:**
Banach space,
boundary value problem,
differential equation,
delay.

##### 3323 On Minimum Cycle Bases of the Wreath Product of Wheels with Stars

**Authors:**
M. M. M. Jaradat,
M. K. Al-Qeyyam

**Abstract:**

The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.

**Keywords:**
Cycle space,
minimum cycle basis,
wreath product.

##### 3322 Optimal Duty-Cycle Modulation Scheme for Analog-To-Digital Conversion Systems

**Authors:**
G. Sonfack,
J. Mbihi,
B. Lonla Moffo

**Abstract:**

This paper presents an optimal duty-cycle modulation (ODCM) scheme for analog-to-digital conversion (ADC) systems. The overall ODCM-Based ADC problem is decoupled into optimal DCM and digital filtering sub-problems, while taking into account constraints of mutual design parameters between the two. Using a set of three lemmas and four morphological theorems, the ODCM sub-problem is modelled as a nonlinear cost function with nonlinear constraints. Then, a weighted least p^{th} norm of the error between ideal and predicted frequency responses is used as a cost function for the digital filtering sub-problem. In addition, MATLAB *fmincon* and MATLAB *iirlnorm *tools are used as optimal DCM and least p^{th} norm solvers respectively. Furthermore, the *virtual simulation* scheme of an overall prototyping ODCM-based ADC system is implemented and well tested with the help of Simulink tool according to relevant set of design data, i.e., 3 KHz of modulating bandwidth, 172 KHz of maximum modulation frequency and 25 MHZ of sampling frequency. Finally, the results obtained and presented show that the ODCM-based ADC achieves under 3 KHz of modulating bandwidth: 57 dBc of SINAD (signal-to-noise and distorsion), 58 dB of SFDR (Surpious free dynamic range) -80 dBc of THD (total harmonic distorsion), and 10 bits of minimum resolution. These performance levels appear to be a great challenge within the class of oversampling ADC topologies, with 2^{nd} order IIR (infinite impulse response) decimation filter.

**Keywords:**
Digital IIR filter,
morphological lemmas and theorems,
optimal DCM-based DAC,
virtual simulation,
weighted least pth norm.

##### 3321 Investigating Feed Mix Problem Approaches: An Overview and Potential Solution

**Authors:**
Rosshairy Abd Rahman,
Chooi-Leng Ang,
Razamin Ramli

**Abstract:**

Feed is one of the factors which play an important role in determining a successful development of an aquaculture industry. It is always critical to produce the best aquaculture diet at a minimum cost in order to trim down the operational cost and gain more profit. However, the feed mix problem becomes increasingly difficult since many issues need to be considered simultaneously. Thus, the purpose of this paper is to review the current techniques used by nutritionist and researchers to tackle the issues. Additionally, this paper introduce an enhance algorithm which is deemed suitable to deal with all the issues arise. The proposed technique refers to Hybrid Genetic Algorithm which is expected to obtain the minimum cost diet for farmed animal, while satisfying nutritional requirements. Hybrid GA technique with artificial bee algorithm is expected to reduce the penalty function and provide a better solution for the feed mix problem.

**Keywords:**
Artificial bee algorithm,
feed mix problem,
hybrid genetic algorithm.

##### 3320 A Study of Under Actuator Dynamic System by Comparing between Minimum Energy and Minimum Jerk Problems

**Authors:**
Tawiwat V.,
Phermsak S.,
Noppasit C.

**Abstract:**

This paper deals with under actuator dynamic systems such as spring-mass-damper system when the number of control variable is less than the number of state variable. In order to apply optimal control, the controllability must be checked. There are many objective functions to be selected as the goal of the optimal control such as minimum energy, maximum energy and minimum jerk. As the objective function is the first priority, if one like to have the second goal to be applied; however, it could not fit in the objective function format and also avoiding the vector cost for the objective, this paper will illustrate the problem of under actuator dynamic systems with the easiest to deal with comparing between minimum energy and minimum jerk.

**Keywords:**
Under actuator,
Dynamic optimal control,
Minimumjerk,
Minimum energy.

##### 3319 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.

##### 3318 Bandwidth Allocation for ABR Service in Cellular Networks

**Authors:**
Khaja Kamaluddin,
Muhammed Yousoof

**Abstract:**

**Keywords:**
Bandwidth allocation,
Virtual Channel (VC),
CBR,
ABR,
MCR and QOS.

##### 3317 The Optimization of Decision Rules in Multimodal Decision-Level Fusion Scheme

**Authors:**
Andrey V. Timofeev,
Dmitry V. Egorov

**Abstract:**

This paper introduces an original method of parametric optimization of the structure for multimodal decisionlevel fusion scheme which combines the results of the partial solution of the classification task obtained from assembly of the mono-modal classifiers. As a result, a multimodal fusion classifier which has the minimum value of the total error rate has been obtained.

**Keywords:**
Сlassification accuracy,
fusion solution,
total error
rate.

##### 3316 Citizenship Norms and the Participation of Young Adults in a Democracy

**Authors:**
Samsudin A. Rahim,
Latiffah Pawanteh,
Ali Salman

**Abstract:**

**Keywords:**
citizenship norms,
political participation,
civic
participation,
youths,
globalization

##### 3315 An Effective Algorithm for Minimum Weighted Vertex Cover Problem

**Authors:**
S. Balaji,
V. Swaminathan,
K. Kannan

**Abstract:**

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

**Keywords:**
Weighted vertex cover,
vertex support,
approximation algorithms,
NP-complete problem.