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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.

    Note   In previous versions of MATLAB® product, the augmented matrix was used by sparse linear equation solvers, \ and /, for nonsquare problems. Now, MATLAB software performs a least squares solve using the qr factorization of A instead.

See Also

Introduced before R2006a

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