A noise-cancellation method, comprising the steps of: receiving a value x(n) from a noise sensor at a time step; storing the received value in a buffer, the buffer having a length N, the buffer further storing a number of additional values, wherein an end value x(n-N) is removed from the buffer to accommodate the received value; providing a previously-computed result A(n-1), wherein the previously-computed result represents the sum of the square of the values stored in the buffer at a previous time step; performing one of: (i) adding a square of the received value to the previously-computed result and subtracting a square of the end value from the sum of the received value and the previously computed value in order to yield a newly-computed result A(n); or (ii) subtracting a square of the end value from the previously-computed result and adding a square of the received value to the result of subtracting the square of the end value from the previously computed result in order to yield a newly-computed result A(n); and updating a plurality of coefficients of an adaptive filter according to, in part, the value of the newly-computed result; generating with the adaptive filter a noise-cancelling signal using the updated plurality of coefficients; and providing the noise-cancellation signal to an actuator for transduction of a noise-cancellation audio signal based on the noise-cancellation signal, the noise-cancellation audio signal destructively interfering with an undesired noise signal in a noise-cancellation zone; wherein the method further comprises the step of, during the time step, summing the square of the values stored in the buffer to yield a corrective value B(n) and replacing the newly-computed result with the corrective value. receiving a value x(n) from a noise sensor at a time step; storing the received value in a buffer, the buffer having a length N, the buffer further storing a number of additional values, wherein an end value x(n-N) is removed from the buffer to accommodate the received value; providing a previously-computed result A(n-1), wherein the previously-computed result represents the sum of the square of the values stored in the buffer at a previous time step; performing one of: (i) adding a square of the received value to the previously-computed result and subtracting a square of the end value from the sum of the received value and the previously computed value in order to yield a newly-computed result A(n); or (ii) subtracting a square of the end value from the previously-computed result and adding a square of the received value to the result of subtracting the square of the end value from the previously computed result in order to yield a newly-computed result A(n); and (i) adding a square of the received value to the previously-computed result and subtracting a square of the end value from the sum of the received value and the previously computed value in order to yield a newly-computed result A(n); or (ii) subtracting a square of the end value from the previously-computed result and adding a square of the received value to the result of subtracting the square of the end value from the previously computed result in order to yield a newly-computed result A(n); and updating a plurality of coefficients of an adaptive filter according to, in part, the value of the newly-computed result; generating with the adaptive filter a noise-cancelling signal using the updated plurality of coefficients; and providing the noise-cancellation signal to an actuator for transduction of a noise-cancellation audio signal based on the noise-cancellation signal, the noise-cancellation audio signal destructively interfering with an undesired noise signal in a noise-cancellation zone; wherein the method further comprises the step of, during the time step, summing the square of the values stored in the buffer to yield a corrective value B(n) and replacing the newly-computed result with the corrective value.