Abstract
We investigate self-testing programs with relative error by allowing error terms proportional to the function to be computed.In the self-testing literature for numerical computations, only absolute errors and sublinear (in the input size) errors were previously studied. We construct new self-testers with relative error for real-valued multi-linear functions defined over finite rational domains. The existence of such self-testers positively solves an open question in [KMS2].
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Magniez, F. Multi-Linearity Self-Testing with Relative Error. Theory Comput Syst 38, 573–591 (2005). https://doi.org/10.1007/s00224-004-1125-y
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DOI: https://doi.org/10.1007/s00224-004-1125-y