# diagonally dominant in a sentence

### Examples

- A sufficient ( but not necessary ) condition for the method to converge is that the matrix " A " is strictly or irreducibly
*diagonally dominant*. - As the coefficients of the discretised equation are always positive hence satisfying the requirements for boundedness and also the coefficient matrix is
*diagonally dominant*therefore no irregularities occur in the solution. - We say A is SDD if all of its rows are SDD . "'Weakly
*diagonally dominant*"'( WDD ) is defined with \ geq instead. - P-SHAKE computes and updates a pre-conditioner which is applied to the constraint gradients before the SHAKE iteration, causing the Jacobian \ mathbf J _ \ sigma to become diagonal or strongly
*diagonally dominant*. - *PM : proof of determinant lower bound of a strict
*diagonally dominant*matrix, id = 9304 new !-- WP guess : proof of determinant lower bound of a strict diagonally dominant matrix-- Status: - *PM : proof of determinant lower bound of a strict diagonally dominant matrix, id = 9304 new !-- WP guess : proof of determinant lower bound of a strict
*diagonally dominant*matrix-- Status: - For a matrix with polynomial entries, one sensible definition of diagonal dominance is if the highest power of q appearing in each row appears only on the diagonal . ( The evaluations of such a matrix at large values of q are
*diagonally dominant*in the above sense .) - Recalling that an irreducible matrix is one whose associated directed graph is strongly connected, a trivial corollary of the above is that an " irreducibly
*diagonally dominant*matrix " ( i . e ., an irreducible WDD matrix with at least one SDD row ) is nonsingular. - Thomas'algorithm is not stable in general, but is so in several special cases, such as when the matrix is
*diagonally dominant*( either by rows or columns ) or symmetric positive definite; If stability is required in the general case, Gaussian elimination with partial pivoting ( GEPP ) is recommended instead. - Similarly, an Hermitian strictly
*diagonally dominant*matrix with real positive diagonal entries is positive definite, as it equals to the sum of some Hermitian diagonally dominant matrix A with real non-negative diagonal entries ( which is positive semidefinite ) and xI for some positive real number x ( which is positive definite ).