Solving Least-Squares Problems via a Double-Optimal Algorithm and a Variant of the Karush–Kuhn–Tucker Equation for Over-Determined Systems

A double optimal solution (DOS) of a least-squares problem Ax=b,A∈Rq×n with q≠n is derived in an m+1-dimensional varying affine Krylov subspace (VAKS); two minimization techniques exactly determine the m+1 expansion coefficients of the solution x in the VAKS. The minimal-norm solution can be obtaine...

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