Interval-constrained matrix balancing
The following two problems are studied: 1. Given a nonnegative (m,n)-matrix \(A=(a_{ij})\) and positive vectors u, v; determine a `nearby' nonnegative (m,n)-matrix \(X=(x_{ij})\) such that \(\sum_{j}x_{ij}=u_ i\), \(i=1,...,m\), \(\sum_{i}x_{ij}=v_ j\), \(j=1,...,n\) and \(x_{ij}>0\) only if \(a_{ij}>0.\) 2. Given the same matrix as above \((m=n)\); find a `nearby' nonnegative matrix X such that \(\sum_{j}x_{ij}=\sum_{j}x_{ji}\), \(i=1,...,n\) and \(x_{ij}>0\) only if \(a_{ij}>0.\) It is considered the entropy optimization approach to define the `nearness' in these problems. A numerical method for solving is given. Numerical experiments illustrate the efficiency and effectiveness of the method and its superior performance when implemented in parallel.
scientific article; zbMATH DE number 4195048
scientific article