Multi-linearity self-testing with relative error

Abstract. We investigate self-testing programs with relative error by allowing error terms proportional to the function to be computed. Until now, in numerical computation, error terms were assumed to be either constant or proportional to the p-th power of the magnitude of the input, for p ∈ [0, 1). We construct new self-testers with relative error for realvalued multi-linear functions defined over finite rational domains. The existence of such self-testers positively solves an open question in [KMS99]. Moreover, our self-testers are very efficient: they use few queries and simple operations

Multi-Linearity Self-Testing with Relative Error

. We investigate self-testing programs with relative error by allowing error terms proportional to the function to be computed. Until now, in numerical computation, error terms were assumed to be either constant or proportional to the p-th power of the magnitude of the input, for p 2 [0; 1). We construct new self-testers with relative error for realvalued multi-linear functions defined over finite rational domains. The existence of such self-testers positively solves an open question in [KMS99]. Moreover, our self-testers are very efficient: they use few queries and simple operations. Keywords --- Program verification, approximation error, self--testing programs, robustness and stability of functional equations. 1 Introduction It is not easy to write a program P to compute a real-valued function f . By definition of floating point computations, a program P can only compute an approximation of f . The succession of inaccuracies in computational operations could be significant..