 # The determinant of Hilbert's matrix

The determinant of Hilbert's matrix (11x11) without pivoting strategy is computed.
After triangularization, the determinant is the product of the diagonal elements.
Hilbert's matrix is defined by: a(i,j) = 1/(i+j-1).

Pivot number 1 = 0.1000000000000000D+01
Pivot number 2 = 0.8333333333333331D-01
Pivot number 3 = 0.5555555555555522D-02
Pivot number 4 = 0.3571428571428736D-03
Pivot number 5 = 0.2267573696146732D-04
Pivot number 6 = 0.1431549050481817D-05
Pivot number 7 = 0.9009749236431395D-07
Pivot number 8 = 0.5659970607161749D-08
Pivot number 9 = 0.3551362553328898D-09
Pivot number 10 = 0.2226656943069665D-10
Pivot number 11 = 0.1398301799864147D-11
Determinant = 0.3026439382718219D-64

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CADNA software --- University P. et M. Curie --- LIP6
Self-validation detection: ON
Mathematical instabilities detection : ON
Branching instabilities detection : ON
Intrinsic instabilities detection : ON
Cancellation instabilities detection : ON
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Pivot number 1 = 0.100000000000000E+001
Pivot number 2 = 0.833333333333333E-001
Pivot number 3 = 0.55555555555555E-002
Pivot number 4 = 0.3571428571428E-003
Pivot number 5 = 0.22675736961E-004
Pivot number 6 = 0.1431549051E-005
Pivot number 7 = 0.90097493E-007
Pivot number 8 = 0.5659970E-008
Pivot number 9 = 0.35513E-009
Pivot number 10 = 0.2226E-010
Pivot number 11 = 0.14E-011
Determinant = 0.30E-064
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CADNA software --- University P. et M. Curie --- LIP6
No instability detected