Computationally simplified numerical algorithms for certain Engineering problems

Abstract

newlineSolving system of linear algebraic equations determining the newlineroots of a real algebraic polynomial and evaluating determinant value of newlinea matrix are ancient problems in engineering applications however there newlineis an increasing demand for computationally stable and efficient newlinenumerical algorithms converging to the actual results of these problems newlineThe proposed research provides novel techniques to enhance newlineconvergence rate of the numerical algorithms to solve these engineering newlineproblems in terms of accuracy and computational time newlineThe condition of these conventional mathematical problems newlinerelates to their sensitivity to the input perturbation A computation is newlinenumerically unstable if the uncertainty of the input values is grossly newlinemagnified by the numerical method When the results of numerical newlinecomputations are extremely critical and cause loss of human life or have newlinesevere economic or social implication it is appropriate to take special newlineprecautions Therefore handling Ill conditioning of these problems and newlineapplying soft computing technique for optimization have been newlineincorporated in the proposed algorithms newline newline