On a nonnegative solution of a system of equations with a nonstrictly Jacobian matrix
The author considers a system of linear equations \(Ax=d\) with a regular tridiagonal matrix \(A\) whose entries satisfy certain nonnegativity conditions. Moreover, \(d\geq 0\). The idea of the article consists in finding a regular matrix \(G\) such that \(GA\) is monotone, i.e., \((GA)x\geq 0\) implies \(x\geq 0\). Then \(Gd\geq 0\) is a sufficient condition for the existence of a nonnegative solution of the system.
scientific article; zbMATH DE number 1023887