Accurate Computations for Some Classes of Matrices
A square matrix is called a P-matrix if all its principal minors are positive. Subclasses of P-matrices with many applications are the nonsingular totally positive matrices and the nonsingular M-matrices. For diagonally dominant M-matrices and some subclasses of nonsingular totally nonnegative matrices, accurate methods for computing their singular values, eigenvalues or inverses have been obtained, assuming that adequate natural parameters are provided. The adequate parameters for diagonally dominant M-matrices are the row sums and the off-diagonal entries, and for nonsingular totally nonnegative matrices are the entries of their bidiagonal factorization. In this paper we survey some recent extensions of these methods to other related classes of matrices.
KeywordsAccurate Computation Gaussian Elimination Nonnegative Matrice Total Positivity Positive Matrice
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