Procrustes problems in finite dimensional indefinite scalar product spaces

Some applications from multidimensional scaling in an environment of indefinite scalar products are investigated. In particular, the construction of points from given distances is considered, and two variants of Procrustes problems are discussed. It is found that both Procrustes problems can be solved with the help of H-polar decompositions or (G, H)-polar decompositions of specified matrices. Furthermore, a method for the numerical computation of H- or (G, H)-polar decompositions of nonsingular matrices is described.