Error sources and error propagation in the Levinson-Durbin algorithm

It is proved that there are two types of numerical error, due to finite precision, in the Levinson-Durbin algorithms; an erratic and a systematic one. The erratic one depends on the value the input autocorrelation accidentally takes at an iteration, and, essentially, it affects only the results obtained at this particular recursion. On the contrary, the systematic numerical error increases with the information the system carries and propagates essentially throughout the algorithm. It is shown that, for both types of error, as well as the overall one, there are specific intermediate quantities, calculated in the evolution of the algorithm, which may serve as precise indicators of the exact number of erroneous digits with which the various quantities are computed including the PARCOR coefficients and the filter coefficients. Therefore, the generated numerical error can be accurately traced.<
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