Householder Orthogonalization with a Nonstandard Inner Product

Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning input. However, context a non-standard inner product, it becomes difficult to apply due lack initial orthonormal basis. We propose strategies overcome this obstacle and discuss algorithms variants with product. Theoretical analysis experiments demonstrate that our approach is numerically stable under mild assumptions.