Abstract. Formal verification of numerical programs is notoriously difficult. On the one hand, there exist automatic tools specialized in floatingpoint arithmetic, such as Gappa...
High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, ...
Florent de Dinechin, Christoph Quirin Lauter, Guil...
Smale's -theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to ...