Square-root free orthogonalization algorithms

This paper is concerned with the derivation and analysis of higher order algorithms of polynomial type for computing an orthonormal basis of a subspace. These algorithms are derived from unconstrained optimization of certain cost functions. The proposed methods are efficient and do not require square root computation. Based on these, algorithms for orthonormalization with respect to a positive definite matrix and principal and minor subspace methods are developed. Numerical experiments illustrate the theoretical results.