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Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem

Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem

A standard method for solving the symmetric definite generalized eigenvalue problem $Ax = \lambda Bx$, where A is symmetric and B is symmetric positive definite, is to compute a Cholesky factorization B = LLT (optionally with complete pivoting) and solve the equivalent standard symmetric eigenvalue problem $C y = \lambda …