Automatic Verification of Right-Greedy Numerical Linear Algebra Algorithms

We present an automatic verification process for formally proving the correctness of a class of greedy numerical linear algebra algorithms. To demonstrate our methodology, we present theorem prover verifications of LU and Cholesky decompositions. We formalize a framework for reasoning about matrices and matrix algorithms by partitioning matrices and developing a generalized form of the inductive invariant common to this class of greedy algorithms. Our framework enables users to readily verify any algorithm in this class automatically by simply defining the algorithm itself and specifying the class of matrices on which the algorithm performs. Our framework is also adaptable to other greedy numerical linear algebra algorithms. To our knowledge, this is the first automatic approach to verifying an entire class of numerical linear algebra algorithms.