Comments on: Cholesky decomposition http://www.tangentspace.net/cz/archives/2006/07/cholesky-decomposition/ somewhere near the beginning. Mon, 01 Dec 2008 23:41:04 +0000 http://wordpress.org/?v=2.5 By: Peter Steeves http://www.tangentspace.net/cz/archives/2006/07/cholesky-decomposition/#comment-75297 Peter Steeves Sat, 09 Dec 2006 02:03:49 +0000 http://www.tangentspace.net/cz/archives/2006/07/cholesky-decomposition#comment-75297 Hi, I am a geomatics Engineer. I began programming Cholesky's algorithms in 1975. In 1977, I was able to solve 250,000 non-linear equations on a B2700 computer that had 128 Kilo Bytes of RAM. I authored "The Block Cholesky." I am able to compute any block of the Inverse Matrix without computing all of the matrix. A Mathematics & Computer Science Professor told me it was impossible to solve the inverse by blocks; therefore, I did it. First man on Earth to do so. Actually, my algorithm is really simple. It solves the matrix by blocking it in 10x10, 20x20, or even 100x100 blocks. Only 3 blocks are required in RAM at any one time. This means my solution is only limited by the size of the hard drive and time. It's quite fast even though it's blocked. I adjusted 400 Kms of leveling data from Northern Nigeria in 0.75 seconds. See if you can find my papers at www.gssGeomatics.com. I'll be adding more real soon. Right now I am developing a Least Squares solutions for leveling, horizontal control, and GPS. Peter Steeves, BSc, MSc, PhD Geomatics Engineer Mississauga, Ontario Canada Hi, I am a geomatics Engineer. I began programming Cholesky’s algorithms in 1975. In 1977, I was able to solve 250,000 non-linear equations on a B2700 computer that had 128 Kilo Bytes of RAM. I authored “The Block Cholesky.” I am able to compute any block of the Inverse Matrix without computing all of the matrix. A Mathematics & Computer Science Professor told me it was impossible to solve the inverse by blocks; therefore, I did it. First man on Earth to do so. Actually, my algorithm is really simple. It solves the matrix by blocking it in 10×10, 20×20, or even 100×100 blocks. Only 3 blocks are required in RAM at any one time. This means my solution is only limited by the size of the hard drive and time. It’s quite fast even though it’s blocked. I adjusted 400 Kms of leveling data from Northern Nigeria in 0.75 seconds.

See if you can find my papers at http://www.gssGeomatics.com. I’ll be adding more real soon. Right now I am developing a Least Squares solutions for leveling, horizontal control, and GPS.

Peter Steeves, BSc, MSc, PhD
Geomatics Engineer
Mississauga, Ontario
Canada

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