Numerical examples 


The gaussian methodIn this example, CADNA is able to provide correct results which were impossible to be obtained with the standard floating point arithmetic.The following linear system is solved with the Gaussian elimination method with partial pivoting. The system is A.X=B with:
Without CADNA:
With CADNA:CADNA software  University P. et M. Curie  LIP6 Selfvalidation detection: ON Mathematical instabilities detection : ON Branching instabilities detection : ON Intrinsic instabilities detection : ON Cancellation instabilities detection : ON 
CADNA software  University P. et M. Curie  LIP6 There are 3 numerical instabilities 0 UNSTABLE DIVISION(S) 0 UNSTABLE POWER FUNCTION(S) 0 UNSTABLE MULTIPLICATION(S) 1 UNSTABLE BRANCHING(S) 0 UNSTABLE MATHEMATICAL FUNCTION(S) 1 UNSTABLE INTRINSIC FUNCTION(S) 1 UNSTABLE CANCELLATION(S) CommentsDuring the reduction of the third column, A(3,3) is equal to 4864. But the exact value of A(3,3) is zero. The standard foating point arithmetic cannot detect that A(3,3) is not significant. This value is chosen as pivot. That leads to erroneous results.CADNA detects the no significant value of A(3,3). This
value is eliminated as pivot. That leads to satisfying results.
