# PageRank

### From Wikimization

(Difference between revisions)

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<pre> | <pre> | ||

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 | ||

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% 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 | ||

</pre> | </pre> | ||

=== 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

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. % % See also SUM % % 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

Accuracy and Stability of Numerical Algorithms, N. Higham, 1996

For multiplier error feedback, see:

Implementation of Recursive Digital Filters for High-Fidelity Audio