Numerical Computation of the Sign of the Determinant
Additive and Multiplicative Preconditioning Approach
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Accurate computation of the sign and the value of a matrix determinant attracts a great deal of attention. Various algebraic and geometric computations boil down to it. This includes the computation of a convex hull and a Voronoi diagram as well as the evaluation and expansion of scalar, univariate and multivariate resultants. In the present day computing environment, it is most effective to compute determinants numerically with IEEE standard double precision floating-point numbers provided rounding errors are controlled. That control is difficult where the input matrix is ill conditioned but ...
Accurate computation of the sign and the value of a matrix determinant attracts a great deal of attention. Various algebraic and geometric computations boil down to it. This includes the computation of a convex hull and a Voronoi diagram as well as the evaluation and expansion of scalar, univariate and multivariate resultants. In the present day computing environment, it is most effective to compute determinants numerically with IEEE standard double precision floating-point numbers provided rounding errors are controlled. That control is difficult where the input matrix is ill conditioned but easy where the matrix is well conditioned. This motivates the application of preconditioning methods. In this book, recent techniques of additive preconditioning are applied, the technicalities of this application are elaborated, and the power of the approach is demonstrated with numerical experiments. That book should be especially useful to professionals in Science and Engineering who are interested about the Numerical Computation approach, technicalities and applications to Matrices.
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