# Accumulator Error Feedback

### From Wikimization

function s_hat=csum(x) % CSUM Sum of elements using a compensated summation algorithm. % % For large vectors, the native sum command in Matlab does % not appear to use a compensated summation algorithm which % can cause significant roundoff errors. % % This code implements a variant of Kahan's compensated % summation algorithm which often takes about twice as long, % but produces more accurate sums when the number of % elements is large. -David Gleich % % See also SUM % % Matlab example: % v=rand(1e7,1); % sum1 = sum(v); % sum2 = csum(v); % fprintf('sum1 = %18.16e\nsum2 = %18.16e\n', sum1, sum2); s_hat=0; y=0; e=0; for i=1:numel(x) s_hat_old = s_hat; y = x(i) + e; s_hat = s_hat_old + y; e = (s_hat_old - s_hat) + y; %calculate difference first (Higham) end

### links

Accuracy and Stability of Numerical Algorithms, Nicholas J. Higham, 1996

For multiplier error feedback, see:

Implementation of Recursive Digital Filters for High-Fidelity Audio

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