Office 2007 Pro Plus Accumulator Error Feedback -
 

CSUM() in Digital Signal Processing terms: z-1 can be a unit delay,Microsoft Office 2010 Standard, Q can be a floating-point quantizer to 64 bits, qi represents error because of quantization (additive by definition).
-Jon Dattorro From Wikimization
function s_hat=csum(x)
percent CSUM Sum of factors employing a compensated summation algorithm.
%
percent For big vectors, the native sum command in Matlab does percent not seem to use a compensated summation algorithm which % could cause considerable roundoff mistakes.
%
% This code implements a variant of Kahan's compensated % summation algorithm which frequently can take about two times as lengthy, % but produces far more accurate sums when the quantity of % aspects is large. -David Gleich
percent
percent See also SUM
%
% Matlab instance:
% v=rand(1e7,Office Professional 2007 Key,1);
% sum1 = sum(v);
% sum2 = csum(v);
percent 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,Office 2007 Pro Plus, Nicholas J. Higham,Office 2010 License, 1996
For multiplier error feedback,Office Professional Plus 2007, see:
Implementation of Recursive Digital Filters for High-Fidelity Audio
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