Nonlinear eigenvector algorithms for local optimization in multivariate data analysis (Q1369295)

The paper considers matrix approximation problems arising in several statistical applications of multivariate data analysis, in particular in reduced rank approximation problems. The paper surveys several local optimization algorithms and discusses convergence properties of an iterative algorithm for a related nonlinear eigenproblem of the form \(R(x)x= \lambda S(x)x\). Several applications as weighted least squares scaling with \(\ell_p\)-distances are discussed.