Computationally simplified numerical algorithms for certain Engineering problems

Abstract

newline Solving system of linear algebraic equations determining the newline roots of a real algebraic polynomial and evaluating determinant value of newline a matrix are ancient problems in engineering applications however there newline is an increasing demand for computationally stable and efficient newline numerical algorithms converging to the actual results of these problems newline.The proposed research provides novel techniques to enhance newline convergence rate of the numerical algorithms to solve these engineering newline problems in terms of accuracy and computational time newline The condition of these conventional mathematical problems newline relates to their sensitivity to the input perturbation A computation is newline numerically unstable if the uncertainty of the input values is grossly newline magnified by the numerical method When the results of numerical newline computations are extremely critical and cause loss of human life or have newline severe economic or social implication it is appropriate to take special newline precautions Therefore handling Ill conditioning of these problems and newline applying soft computing technique for optimization have been newline incorporated in the proposed algorithms newline newline