Search for full QR decomposition with reduced QR

Question

What is the best way to find additional orthonormal Q columns? I have already calculated the reduced QR decomposition, but I need a complete QR decomposition.

I assume there is a standard approach to this, but I had trouble finding it.

You may wonder why I need a full Q-matrix. I use it to apply a constraint matrix for "natural" splines to a shortened extension of the base series. I am doing this in Java, but looking for a language independent answer.

Answer 1

Add the columns in Q sequentially as follows:

• Select a vector that is not yet in Q
• Orthogonalize it by Q columns
• Q.
• R

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