# PageRank

(Difference between revisions)
 Revision as of 14:26, 3 March 2009 (edit)← Previous diff Revision as of 14:33, 3 March 2009 (edit) (undo)Next diff → Line 4: Line 4:

function s_hat=csum(x)                                                                                                                                                                                                                                            function s_hat=csum(x)
-                                                         % CSUM Sum of elements using a compensated summation algorithm                                                                                                                                       +                                                            % CSUM Sum of elements using a compensated summation algorithm.
+                                                            % David Gleich, Stanford University, 2008
%                                                                                                                                                                                                                                                                 %
% For large vectors, the native sum command in Matlab does                                                                                                                                                                                                        % For large vectors, the native sum command in Matlab does
Line 22:                                                                                                                                                                                                                                                       Line 23:
%   sum2 = csum(v);                                                                                                                                                                                                                                               %   sum2 = csum(v);
%   fprintf('sum1 = %18.16e\nsum2 = %18.16e\n', sum1, sum2);                                                                                                                                                                                                      %   fprintf('sum1 = %18.16e\nsum2 = %18.16e\n', sum1, sum2);
-
-                                                         % David Gleich, Stanford University, 2008

s_hat=0; y=0; e=0;                                                                                                                                                                                                                                                s_hat=0; y=0; e=0;
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y = x(i) + e;                                                                                                                                                                                                                                                     y = x(i) + e;
s_hat = s_hat_old + y;                                                                                                                                                                                                                                            s_hat = s_hat_old + y;
-                                                         e = (s_hat_old - s_hat) + y;  %calculate difference first                                                                                                                                            +                                                            e = (s_hat_old - s_hat) + y;  %calculate difference first (Higham)
end                                                                                                                                                                                                                                                               end

=== links === === links === - [http://www.google.com/books?id=FJyBjjtHREQC&dq=Accuracy+and+Stability+of+Numerical+Algorithms&printsec=frontcover&source=bn#PPA92,M1 Accuracy and Stability of Numerical Algorithms, Higham, 1996] + [http://www.google.com/books?id=FJyBjjtHREQC&dq=Accuracy+and+Stability+of+Numerical+Algorithms&printsec=frontcover&source=bn#PPA92,M1 Accuracy and Stability of Numerical Algorithms, N. Higham, 1996] For multiplier error feedback, see: For multiplier error feedback, see:

## Revision as of 14:33, 3 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.
% David Gleich, Stanford University, 2008
%
% 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);

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
```