ABSTRACT
Many engineering and scientific problems can be formulated in terms of systems of simultaneous linear equations. An important consideration in solving systems of simultaneous equations using either Gaussian or Gauss–Jordan elimination is a loss of precision caused by accumulated roundoff errors in the numerical calculations. Problems with roundoff and truncation are most likely to occur when the coefficients in the equations differ by several orders of magnitude. The elimination methods described can be used to solve simultaneous equations with banded coefficient matrices. Elimination methods like the Gaussian elimination procedure are often called direct equation-solving methods because the solution is found after a fixed, predictable number of operations. A number of iteration methods are available for solving simultaneous equations. The chapter reviews the substitution method for obtaining an analytical solution in order to illustrate the need for numerical methods.
