Diagonally Perturbing a Symmetric Matrix to Make It Positive Definite

Suppose is a matrix that is symmetric but not positive definite. What is the best way to perturb the diagonal to make positive definite? We want to compute a vector such that is positive definite. Since the positive definite matrices form an open set there is no minimal , so we relax the requirement to … Continue reading Diagonally Perturbing a Symmetric Matrix to Make It Positive Definite