# PageRank

(Difference between revisions)
 Revision as of 00:23, 4 March 2009 (edit) (→links)← Previous diff Revision as of 15:25, 5 March 2009 (edit) (undo) (Removing all content from page)Next diff → Line 1: Line 1: - [[Image:Gleich.jpg|thumb|right|429px|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
-
- - === 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, Nicholas J. Higham, 1996] - - 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 the above...]