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Gram-Schmidt

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Gram-Schmidt

03 Feb 2010

Gram-Schmidt algorithm to orthonormalize a set of vectors.

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Description	The set of vectors is passed like column vectors of a matrix. This algorithm take advantage of the matrix form using sub matrix (more vectors at the same time). I've tested it with a random 1000x1000 matrix (so 1000 vectors 1000x1) giving a result in 7.4863 sec (mean value on 5 executions... best time 7.2321)
MATLAB release	MATLAB 7 (R14)

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Everyone's Tags	gramschmidt, mathematics, orthogonalization, orthonormalization
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Comments and Ratings (2)
03 Feb 2010	Vito Tafuni	I think QR performs better on square matrices: A=rand(500,500); t=time;[Q,R]=qr(A);time-t ans = 0.18440 t=time;O=grsm(A);time-t ans = 0.60662 A=rand(500,10); t=time;[Q,R]=qr(A);time-t ans = 0.020872 t=time;O=grsm(A);time-t ans = 0.0041921
03 Feb 2010	Mo Chen	why not use QR