mathnet - QR decomposition in Math.NET Numerics -

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how qr decomposition implemented in math.net numerics?

is gram-schimdt or givens rotations? have feeling implemented gram-schimdt, i'm not sure. can't find implementation.

is qr decomposition gram-schimdt different givens rotations, in terms of results?

i generated (manually) qr decomposition using givens rotations matrix, , generated qr decomposition usingmathnet.numerics.linearalgebra.generic.factorization.qrmethod (which believe implements gram-schimdt) , results different. difference between numbers 1e-16 (not big), , rows have opposite sign (*-1) (this real problem - think happens because mathnet.numerics implements different qr algorithm).

can suggest libraries perform qr decomposition using givens rotations?

according documentation, implemented using householder reflections:

the computation of qr decomposition done @ construction time householder transformation.

different methods can produce answers small numerical differences or negative rows, describe. see wikipedia article more information.


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