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Semi-numerical Iterative Series Solution of Linear Algebraic Equations with Mathematica

N. Ioakimidis
Journal / Anthology

Communications in Applied Numerical Methods
Year: 1992
Volume: 8
Page range: 421-429

The computer algebra system MATHEMATICA is applied to the iterative solution of systems of linear algebraic equations where the matrix of the coefficients depends on a parameter. The solution is found in a Taylor-Maclaurin series form with respect to this parameter at an appropriate point and, therefore, the system can be solved only once and for all even if the parameter varies. All three popular iterative methods, that is, the Gauss-Jacobi, the Gauss-Seidel and the successive overrelaxation method are used in particular applications. The complete MATHEMATICA procedure for the last of these methods is also presented. Two elementary applications to structural mechanics are also made and further possibilities are discussed.

*Engineering > Mechanical and Structural Engineering