Accelerometers are supposed to be physical instruments for measuring the acceleration of a moving object. Although huge technological advance is made in hardware of accelerometers over more than one century, accelerometers have been persistently designed and fabricated mechanically under the framework of forward problems of damped mass-spring systems. However, accelerometers are essentially inverse ill-posed source problems from the mathematical point of view, implying that small measurement errors of equivalent displacements are inherently amplified significantly such that accelerations output from accelerometers can become extremely noisy, numerically incorrect and physically meaningless in the case of high sampling rates. The ill-posedness of accelerometers cannot be rigorously solved mechanically but is always implicitly circumvented approximately. As a result, accelerometers theoretically can only produce approximate outputs of acceleration. Here we present the concept of computerized accelerometers in distinguishment of mechanical ones by applying regularization to compute accelerations from equivalent displacements. The acceleration is rigorously reconstructed mathematically as a solution to the inverse ill-posed source problem of acceleration. The concept of computerized accelerometers theoretically warrants precise measurement of acceleration without approximation, is valid for nonlinear damping as well and provides a turning point for accelerometers from a mechanical approximation to a fully rigorous computerized instrument.

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