Explore using thin-QR (Cholesky decompositions) for Gram-Schmidt

[weinbe2]

Instead of using a traditional implementation of classical or modified Gram-Schmidt (or a hybrid thereof), (block-)orthonormalization can be formulated as a thin QR, which is implemented in practice via a Cholesky decomposition of the "outer-product-of-inner-products" of the vectors that are meant to be orthonormalized. This is described in https://arxiv.org/pdf/1801.07823.pdf , right around eqn (5.2). The benefit of this approach would be the numerical stability of a Cholesky decomposition, plus the overhead-reduction properties of batched inner products.