Goal-Oriented and Modular Stability Analysis

We introduce a methodology for obtaining inventories of error results for families of numerical dense linear algebra algorithms. The approach for deriving the analyses is goal-oriented, systematic, and layered. The presentation places the analysis side-by-side with the algorithm so that it is obvious where roundoff error is introduced. The approach supports the analysis of more complex algorithms, such as the blocked LU factorization. For this operation we derive a tighter error bound than has been previously reported in the literature.