A fast and stable test to check if a weakly diagonally dominant matrix is a nonsingular M-matrix
نویسندگان
چکیده
منابع مشابه
A fast and stable test to check if a weakly diagonally dominant matrix is an M-matrix
We present a test for determining if a substochastic matrix is convergent. By establishing a duality between weakly chained diagonally dominant (w.c.d.d.) Lmatrices and convergent substochastic matrices, we show that this test can be trivially extended to determine whether a weakly diagonally dominant (w.d.d.) matrix is a nonsingular M-matrix. The test’s runtime is linear in the order of the in...
متن کاملA stable test to check if a matrix is a nonsingular M-matrix
A stable test for checking if a matrix is a nonsingular M -matrix is presented. Its computational cost is, in the worst case, O(n2) elementary operations higher than the computational cost of Gaussian elimination. The test can be applied to check if a nonnegative matrix has spectral radius less than 1.
متن کاملA stable iteration to the matrix inversion
The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...
متن کاملA New Criteria for a Matrix is not Generalized Strictly Diagonally Dominant Matrix
Generalized strictly diagonally dominant matrix play an important role in numerical algebra, control theory, electric system, economic mathematics and elastic dynamics and so on. But it isn’t easy to determine whether a matrix is or not a generalized strictly diagonally dominant matrix in reality. In this paper, we obtained some new results about a matrix is not generalized strictly diagonally ...
متن کاملGaussian elimination is stable for the inverse of a diagonally dominant matrix
Let B ∈Mn(C) be a row diagonally dominant matrix, i.e., σi|bii| = n ∑ j=1 j 6=i |bij |, i = 1, . . . , n, where 0 ≤ σi < 1, i = 1, . . . , n, with σ = max1≤i≤n σi. We show that no pivoting is necessary when Gaussian elimination is applied to A = B−1. Moreover, the growth factor for A does not exceed 1 + σ. The same results are true with row diagonal dominance being replaced by column diagonal d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2018
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3347