PageRank
From Wikimization
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- | [[Image:Gleich.jpg|thumb|right| | + | [[Image:Gleich.jpg|thumb|right|429px|CSUM() in Digital Signal Processing terms: |
Q is a floating-point quantizer to 64 bits, z<sup>-1</sup> is a unit delay, | Q is a floating-point quantizer to 64 bits, z<sup>-1</sup> is a unit delay, | ||
q<sub>i</sub> represents error due to quantization (additive by definition). -Jon Dattorro]] | q<sub>i</sub> represents error due to quantization (additive by definition). -Jon Dattorro]] |
Revision as of 18:39, 18 February 2009
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. % % See also SUM % % 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