Diagonal Scaling to an Orthogonal Matrix
Abraham Berman, Beresford Ν. Parlett, Robert J. Plemmons · SIAM Journal on Algebraic and Discrete Methods · 1981
An algorithm is given which determines whether a matrix A is diagonally equivalent to an orthogonal matrix and, if so, computes the corresponding scaling factors. The algorithm makes use of the Hadamard quotient $A^{ - 1} \odiv A^t $. Such problems arise, for example, in the study of energy conserving norms for the solution of hyperbolic systems of partial differential equations.