A Computationally Simplified Numerical Algorithm for Evaluating a Determinant
A computationally simplified new procedure is presented in this paper to evaluate the determinant of a matrix A [nxn], where A may be ill-conditioned. The proposed method reduces the nth order determinant using the elementary row operations into a sequence of column vectors and then the determinant is evaluated by multiplying the elements of all column vectors. We improve the condition of ill-conditioned determinant first and then evaluate the well-conditioned one. This procedure is direct and simple in application compared to Gauss reduction method. Both the procedures are applied to illustrative examples and the comparison is also reported.
KeywordsDeterminant Ill-Conditioned Determinant Well-Conditioned Determinant Column Vectors Computational complexity
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