On Factor Width and Symmetric H-matrices
نویسندگان
چکیده
We define a matrix concept we call factor width. This gives a hierarchy of matrix classes for symmetric positive semidefinite matrices, or a set of nested cones. We prove that the set of symmetric matrices with factor width at most two is exactly the class of (possibly singular) symmetric H-matrices (also known as generalized diagonally dominant matrices) with positive diagonals, H+. We prove bounds on the factor width, including one that is tight for factor widths up to two, and pose several open questions.
منابع مشابه
Factor Widths of Nonnegative Matrices
Factor widths of nonnegative integral positive semidefinite square matrices are investigated. The nonnegative factor width, the exact factor width and the binary factor width of such matrices are introduced. Some lower and upper bounds for these widths are obtained. Nonnegative symmetric (completely positive) matrices with some given nonnegative (binary) factor widths
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