A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection.

The study focuses primarily on Vandermonde-like matrix systems. The idea is to express Vandermonde and Vandermonde-like matrix systems as the problems related to Krylov Matrices. The connection provides a different angle to view the Vandermonde-like systems. Krylov subspace methods are strongly related to polynomial spaces, hence a nice connection can be established using LU factorization as proposed by Bjorck and Pereyra and QR factorization by Reichel. Further an algorithm to generate a preconditioner is incorporated in GR algorithm given by Reichel . This generates a preconditioner for Vandermonde-like matrices consisting of polynomials which obey a three term recurrence relation. This general preconditioner works effectively for Vandermonde matrices as well. The preconditioner is then tested on various distinct nodes. Based on results obtained, it is established that the condition number of Vandermonde -like matrices can be lowered significantly by application of the preconditioner, for some cases

Techniques to Enhance Lifetime of Wireless Sensor Networks: A Survey

Increasing lifetime in wireless sensor networks is a major challenge because the nodes are equipped with low power battery. For increasing the lifetime of the sensor nodes energy efficient routing is one solution which minimizes maintenance cost and maximizes the overall performance of the nodes. In this paper, different energy efficient routing techniques are discussed. Here, photovoltaic cell for efficient power management in wireless sensor networks is also discussed which are developed to increase the lifetime of the nodes. Efficient battery usage techniques and discharge characteristics are then described which enhance the operational battery lifetime

NOVEL BORON COMPLEXES DERIVED FROM CATECHOL AND ARYLAZONAPTHOLS

ABSTRACT The reaction of 2-isopropoxy-1,3,2-benzodioxaborole with arylazonapthols in molar ratio 1:1 in benzene gives mixed ligand boron spirochelate

Multigrid solution of distributed optimal control problems constrained by semilinear elliptic PDEs

Optimization constrained by partial differential equations (PDEs) is a research area in which the scientific and engineering communities have seen a growing interest over the last decade. The recent rise in interest was fostered by the tremendous increase in computing power over the last twenty years. This can be attributed both to the tremendous advances in high-performance computing technologies and to its wide range of applicability. However, just growth in computing power is insufficient for tackling PDE-constrained optimization problems and there is always a need for ever-increasing efficient algorithms. The objective of this dissertation is to develop, analyze and implement multigrid preconditioners for the linear systems arising in the Newton-Krylov solution process for the nonlinear PDE constraints. Our main focus is on semilinear elliptic constraints with no additional control or state constraints. We analyze the preconditioners both theoretically and numerically. In this work we show that the multigrid preconditioners are of optimal order (p = 2) for piecewise linear finite element approximations. We also study control-constrained optimal control problems constrained by linear-elliptic equations. This problem is non-trivial from the optimization point of view as the KKT system is now a complementarity system. We employ semismooth Newton methods (SSNMs) to solve this problem efficiently. The multigrid preconditioners discussed here are extensions of preconditioners developed previously for the unconstrained case. We present some new results and techniques that yield optimal order multigrid preconditioners, at least for the case when the control is discretized using piecewise-constant finite elements

Multigrid solution of distributed optimal control problems constrained by semilinear elliptic PDEs

Optimization constrained by partial differential equations (PDEs) is a research area in which the scientific and engineering communities have seen a growing interest over the last decade. The recent rise in interest was fostered by the tremendous increase in computing power over the last twenty years. This can be attributed both to the tremendous advances in high-performance computing technologies and to its wide range of applicability. However, just growth in computing power is insufficient for tackling PDE-constrained optimization problems and there is always a need for ever-increasing efficient algorithms. The objective of this dissertation is to develop, analyze and implement multigrid preconditioners for the linear systems arising in the Newton-Krylov solution process for the nonlinear PDE constraints. Our main focus is on semilinear elliptic constraints with no additional control or state constraints. We analyze the preconditioners both theoretically and numerically. In this work we show that the multigrid preconditioners are of optimal order (p = 2) for piecewise linear finite element approximations. We also study control-constrained optimal control problems constrained by linear-elliptic equations. This problem is non-trivial from the optimization point of view as the KKT system is now a complementarity system. We employ semismooth Newton methods (SSNMs) to solve this problem efficiently. The multigrid preconditioners discussed here are extensions of preconditioners developed previously for the unconstrained case. We present some new results and techniques that yield optimal order multigrid preconditioners, at least for the case when the control is discretized using piecewise-constant finite elements

Multigrid solution of distributed optimal control problems constrained by semilinear elliptic PDEs

Optimization constrained by partial differential equations (PDEs) is a research area in which the scientific and engineering communities have seen a growing interest over the last decade. The recent rise in interest was fostered by the tremendous increase in computing power over the last twenty years. This can be attributed both to the tremendous advances in high-performance computing technologies and to its wide range of applicability. However, just growth in computing power is insufficient for tackling PDE-constrained optimization problems and there is always a need for ever-increasing efficient algorithms. The objective of this dissertation is to develop, analyze and implement multigrid preconditioners for the linear systems arising in the Newton-Krylov solution process for the nonlinear PDE constraints. Our main focus is on semilinear elliptic constraints with no additional control or state constraints. We analyze the preconditioners both theoretically and numerically. In this work we show that the multigrid preconditioners are of optimal order (p = 2) for piecewise linear finite element approximations. We also study control-constrained optimal control problems constrained by linear-elliptic equations. This problem is non-trivial from the optimization point of view as the KKT system is now a complementarity system. We employ semismooth Newton methods (SSNMs) to solve this problem efficiently. The multigrid preconditioners discussed here are extensions of preconditioners developed previously for the unconstrained case. We present some new results and techniques that yield optimal order multigrid preconditioners, at least for the case when the control is discretized using piecewise-constant finite elements

Advanced detection of fungi-bacterial diseases in plants using modified deep neural network and DSURF

Food is indispensable for humans as their growth and survival depend on it. But nowadays, crop is getting spoiled due to fungi and bacteria as soil temperature are changes very rapidly according to sudden climate changes. Due to fungi-bacterial crop, the quality of food is declining day by day and this is really not good for human health. The goal of this research paper is the advanced detection of fungi-bacterial diseases in plants using modified deep neural network approach and DSURF method in order to enhance the detection process. Proposed approach of this research is to use the artificial intelligence techniques like neural network model and dynamic SURF method in order to identify and classify the plant diseases for fungus and bacteria. Additionally, support dynamic feature extraction DSURF & classifier combinations for creating image clusters with the help of Clustering. Deep learning model is employed for training and testing the classifier. The quantitative experimental results of this research work are claimed that authors have achieved the 99.5% overall accuracy by implementing DNNM and DSURF which is much higher than other previous proposed methods in this field. This proposed work is a step towards finding the best practices to detect plant diseases from any bacterial and fungal infection so that humans can get healthy food