FINDING NORMS OF HADAMARD MULTIPLIERS

The norm of a matrix B as a Hadamard multiplier is the norm of the map X --> X . B, where is the Hadamard or entrywise product of matrices. Watson proposed an algorithm for finding lower bounds for the Hadamard multiplier norm of a matrix. It is shown how Watson's algorithm can b e used to give upper bounds as well, which, in many cases, yield the H adamard multiplier norm to any desired accuracy. A sharp form of Witts tock's decomposition theorem is proved for the special case of Hadamar d multiplication.