# PageRank

(Difference between revisions)
 Revision as of 18:48, 18 February 2009 (edit)← Previous diff Revision as of 16:53, 2 March 2009 (edit) (undo)Next diff → Line 33: Line 33: end end + + === links === + For multiplier error feedback, see: + + [http://www.stanford.edu/~dattorro/HiFi.pdf Implementation of Recursive Digital Filters for High-Fidelity Audio] + + [http://www.stanford.edu/~dattorro/CorrectionsHiFi.pdf Comments on...]

## Revision as of 16:53, 2 March 2009 CSUM() in Digital Signal Processing terms: z-1 is a unit delay, Q is a floating-point quantizer to 64 bits, qi represents error due to quantization (additive by definition).
-Jon Dattorro
```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.
%
%
% Example:
%   v=rand(1e7,1);
%   sum1 = sum(v);
%   sum2 = csum(v);
%   fprintf('sum1 = %18.16e\nsum2 = %18.16e\n', sum1, sum2);

% David Gleich, Stanford University, 2008

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;
end
```