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We introduce in this paper the recursive Hessian sketch, a new adaptive filtering algorithm based on sketching the same exponentially weighted least squares problem solved by the recursive least squares algorithm. The algorithm maintains a number of sketches of the inverse autocorrelation matrix and recursively updates them at random intervals. These are in turn used to update the unknown filter estimate. The complexity of the proposed algorithm compares favorably to that of recursive leastdoi:10.1109/icassp.2016.7471659 dblp:conf/icassp/ScheiblerV16 fatcat:zjd7iw663fbxtccuqv75uaujfi