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Scaling Matrices to Prescribed Row and Column Maxima
A nonnegative symmetric matrix $B$ has row maxima prescribed by a given vector $r$, if for each index $i$, the maximum entry in the $i$th row of $B$ equals $r_i$. This paper presents necessary and sufficient conditions so that for a given nonnegative ...
Triangular Factorization of Strongly Row (Column) Full Rank Linear Equations
CIS '14: Proceedings of the 2014 Tenth International Conference on Computational Intelligence and SecurityFirst, the paper gives the definition of the strongly row (column) full rank matrix, the quasi-upper triangular matrix and the quasi-lower triangular matrix of the m n matrix. Then the triangular factorization is generalized to the m n matrix, and some ...
Computing Row and Column Counts for Sparse QR and LU Factorization
AbstractWe present algorithms to determine the number of nonzeros in each row and column of the factors of a sparse matrix, for both the QR factorization and the LU factorization with partial pivoting. The algorithms use only the nonzero structure of the ...






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