Multiplier is an important circuit used in electronic industry especially in digital signal processing operations such as filtering, convolution and analysis of frequency. There are different types of algorithms used in multipliers to achieve better performance. Array multiplier and Wallace tree multiplier are such types of multipliers constructed by using CMOS logic styles such as Swing Restor...

In a modern day CPU, the multiplier has become an important part of an ALU in terms of both power and performance. Modern day multiplier designs provide some enhancements in power and performance over traditional multiplier designs. However, this enhancement, especially from a power perspective, may prove to be inadequate for a low-power application. Using lookup-based tables for multiplication...

Public-key cryptography plays an important role in digital communication and storage systems. Processing public-key cryptosystems requires huge amount of computation, and, there is therefore, a great demand for developing dedicated hardware to speed up the computations. In this thesis, we focus on modular arithmetic hardware algorithms for public-key cryptosystem since these two operations are ...

We consider the application of a variable V-cycle multigrid algorithm for the hybridized mixed method for second order elliptic boundary value problems. Our algorithm differs from previous works on multigrid for the mixed method in that it is targeted at efficiently solving the matrix system for the Lagrange multiplier of the method. Since the mixed method is best implemented by first solving f...

In this talk, we present a trust region method for solving equality constrained optimization problems, which is motivated by the famous augmented Lagrangian function. It is different from standard augmented Lagrangian methods where the augmented Lagrangian function is minimized at each iteration. This method, for fixed Lagrange multiplier and penalty parameters, tries to minimize an approximate...

It is well known that the conventional edge element method in solving vector Maxwell’s eigenvalue problem will lead to the presence of nonphysical zero eigenvalues. This paper uses the mixed finite element method to suppress the presence of these nonphysical zero eigenvalues for 2D vector Maxwell’s eigenvalue problem in anisotropic media. We introduce a Lagrangian multiplier to deal with the co...

This paper proposes a new fast method for calculating modular multiplication. The calculation is performed using a new representation of residue classes modulo M that enables the splitting of the multiplier into two parts. These two parts are then processed separately, in parallel, potentially doubling the calculation speed. The upper part and the lower part of the multiplier are processed usin...

Physical limitations of Complementary Metal-Oxide-Semiconductors (CMOS) technology at nanoscale and high cost of lithography have provided the platform for creating Quantum-dot Cellular Automata (QCA)-based hardware. The QCA is a new technology that promises smaller, cheaper and faster electronic circuits, and has been regarded as an effective solution for scalability problems in CMOS technolog...

In this monograph we develop the function space method for optimization problems and operator equations in Banach spaces. Optimization is the one of key components for mathematical modeling of real world problems and the solution method provides an accurate and essential description and validation of the mathematical model. Optimization problems are encountered frequently in engineering and sci...

Recent advances in mobile computing and multimedia applications demand high-performance and lowpower VLSI Digital Signal Processing (DSP) systems. One of the most widely used operations in DSP is Finite-Impulse Response (FIR) filtering. In the existing method FIR filter is designed using array multiplier, which is having higher delay and power dissipation. The proposed method presents a program...