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Form least-squares augmented system


S = spaugment(A,c)
S = spaugment(A)


S = spaugment(A,c) creates the sparse, square, symmetric indefinite matrix S = [c*I A; A' 0]. The matrix S is related to the least-squares problem

min norm(b - A*x)


r = b - A*x
S * [r/c; x] = [b; 0]

The optimum value of the residual scaling factor c, involves min(svd(A)) and norm(r), which are usually too expensive to compute.

S = spaugment(A) without a specified value of c, uses max(max(abs(A)))/1000.


In previous versions of MATLAB®, the augmented matrix was used by sparse linear equation solvers, \ and /, for nonsquare problems. Now, MATLAB calculates a least-squares solution using the qr factorization of A.

Extended Capabilities

Version History

Introduced before R2006a

See Also