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Welcome to the IUP Journal of Computational Mathematics

Previous Issues

The IUP Journal of Computational Mathematics is a quarterly journal aimed at publishing research contributions of high standard from thought-provoking scientists, eminent academicians and promising researchers, in any or all areas where mathematics and computation interact. The Journal is not confined to meet the needs of one particular research community but is devoted to research articles in diversified areas of computational mathematics.

  • Computational Methods in Linear Algebra
  • Optimization, Ordinary and Partial Differential Equations
  • Approximation Theory
  • Stochastic Models in Finance and Economics
  • Non-Linear Dynamical Systems
  • Fuzzy Logic
  • Neural Nets and Genetic Algorithms
  • Computational Complexity
  • Cryptography, Automata Theory
  • Category Theory
  • Continuum Mechanics
  • Application of Computational Techniques in Science and Engineering
  • Mathematical Theories Underlying Numerical Methods
  • Mathematical Models in Earth Science, Medicine and Environmental Studies
A Note on the Solution of the Nearest Correlation Matrix Problem by Von Neumann Matrix Divergence
Efficient Simulation of the Wishart Model
Online PID Controller Tuning Using Fuzzy Logic Controller
Numerical Solution of Run-Up Flow Through a Pipe with an Equilateral Triangular Cross-Section
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(March 2012)

A Note on the Solution of the Nearest Correlation Matrix Problem by Von Neumann Matrix Divergence

-- S K Mishra

In the extant literature a suggestion has been made to solve the nearest correlation matrix problem by a modified von Neumann approximation. This paper shows that obtaining the nearest positive semi-definite matrix from a given non-positivesemi- definite correlation matrix by such a method is either infeasible or suboptimal. First, if a given matrix is already positive semi-definite, there is no need to obtain any other positive semi-definite matrix closest to it. But when the given matrix is non-positive-semi-definite (Q), then a positive semi-definite matrix closest to it is needed. Then the proposed procedure fails in the absence of log(Q). But if the negative eigenvalue of Q is replaced by a zero/near-zero value, a positive semidefinite matrix is obtained, but it is not nearest to the Q matrix; there are indeed other procedures to obtain better approximation. However, the modified von Neumann approximation method yields results (although sub-optimal) and is, perhaps, one of the fastest methods most suitable to deal with larger matrices. Yet, an alternative algorithm (Fortran program available at http://www.webng.com/ economics/ncor1.txt) is provided to obtain a positive (semi-) definite matrix that performs (speed as well as accuracy-wise) much better.

Article Price : Rs.50

Efficient Simulation of the Wishart Model

-- Pierre Gauthier and Dylan Possamaï

In financial mathematics, Wishart processes have emerged as efficient tools to model stochastic covariance structures. Their numerical simulation may be quite challenging since they involve matrix processes. In this article, we propose an extensive study of financial applications of Wishart processes. First, we derive closed-form formulas for option prices in the single-asset case. Then, we show the relationship between Wishart processes and Wishart law. Finally, we review the existing discretization schemes (Euler and Ornstein-Uhlenbeck) and propose a new scheme, adapted from Heston’s QEM discretization scheme. Extensive numerical results support our comparison of these three schemes.

Article Price : Rs.50

Online PID Controller Tuning Using Fuzzy Logic Controller

-- Elijah E Omizegba, Stephen Bassi, Ejike C Anene and Usman U Abraham

In this work, a discrete Proportional-Integral-Derivative (PID) controller was trained using a Tagaki-Sugeno type fuzzy logic system. The PID parameters were acquired online without the need for manual tuning, calibration or prior knowledge of plant parameters. The developed system has the advantage of fast action and can be easily implemented with a Peripheral Interface Controller (PIC) integrated circuit. Simulation results show that the required PID gains can be acquired in less than 0.03 seconds.

Article Price : Rs.50

Numerical Solution of Run-Up Flow Through a Pipe with an Equilateral Triangular Cross-Section

-- S Raji Reddy

This paper deals with the numerical solution of the run-up flow of a viscous incompressible fluid through a pipe whose cross-section is an equilateral triangle. The problem is solved numerically, using a five-point formula. From this, it is observed that Reynold number has a great influence on the run-up flows. If it is large, the fluid comes to rest after a long time. It is also observed that on the line y = 2h, the decrease in velocity is nose symmetrical in the region. The region y > 4h is the region of silence. Hence it is concluded that Reynold numbers play an important role in run-up flows.

Article Price : Rs.50




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Automated Teller Machines (ATMs): The Changing Face of Banking in India

Bank Management
Information and communication technology has changed the way in which banks provide services to its customers. These days the customers are able to perform their routine banking transactions without even entering the bank premises. ATM is one such development in recent years, which provides remote banking services all over the world, including India. This paper analyzes the development of this self-service banking in India based on the secondary data.

The Information and Communication Technology (ICT) is playing a very important role in the progress and advancement in almost all walks of life. The deregulated environment has provided an opportunity to restructure the means and methods of delivery of services in many areas, including the banking sector. The ICT has been a focused issue in the past two decades in Indian banking. In fact, ICTs are enabling the banks to change the way in which they are functioning. Improved customer service has become very important for the very survival and growth of banking sector in the reforms era. The technological advancements, deregulations, and intense competition due to the entry of private sector and foreign banks have altered the face of banking from one of mere intermediation to one of provider of quick, efficient and customer-friendly services. With the introduction and adoption of ICT in the banking sector, the customers are fast moving away from the traditional branch banking system to the convenient and comfort of virtual banking. The most important virtual banking services are phone banking, mobile banking, Internet banking and ATM banking. These electronic channels have enhanced the delivery of banking services accurately and efficiently to the customers. The ATMs are an important part of a bank’s alternative channel to reach the customers, to showcase products and services and to create brand awareness. This is reflected in the increase in the number of ATMs all over the world. ATM is one of the most widely used remote banking services all over the world, including India. This paper analyzes the growth of ATMs of different bank groups in India.
International Scenario

If ATMs are largely available over geographically dispersed areas, the benefit from using an ATM will increase as customers will be able to access their bank accounts from any geographic location. This would imply that the value of an ATM network increases with the number of available ATM locations, and the value of a bank network to a customer will be determined in part by the final network size of the banking system. The statistical information on the growth of branches and ATM network in select countries.

Indian Scenario

The financial services industry in India has witnessed a phenomenal growth, diversification and specialization since the initiation of financial sector reforms in 1991. Greater customer orientation is the only way to retain customer loyalty and withstand competition in the liberalized world. In a market-driven strategy of development, customer preference is of paramount importance in any economy. Gone are the days when customers used to come to the doorsteps of banks. Now the banks are required to chase the customers; only those banks which are customercentric and extremely focused on the needs of their clients can succeed in their business today.