Start Updating the qr factorization and the least squares problem

Updating the qr factorization and the least squares problem

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The modern approach is to factor the rectangular m × n coefficient matrix A into a product of diagonal, triangular, and orthogonal matrices.

I posted one essay about the puzzle and another one describing its solution.

The second puzzle, 50/50, is considered one of the most difficult hunt puzzles ever.

We find that not only can this save a considerable amount of time when solving least squares problems but the algorithm is also very easy to implement.

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One tweak is the equivalent of pivoting in LU factorization, where during the factorization columns are swapped (swapping rows turns out to change the least squares problem to have a different solution, so column pivoting is used instead).

In this paper we study how to update the solution of the linear system Ax = b after the matrix A is changed by addition or deletion of rows or columns.

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