Appendix 2B: Proof that the least-squares minimization of a constrained model is equal to the least-squares minimization of an unconstrained model of projected data on the space where the constraint is valid.. Appendix 1: Orthogonality between the column spaces of the matrices in equation [5] 133 6.8.2 Appendix 2: Proof that the least-squares minimization of a constrained model is equal to the ...

We consider the problem of choice of norms in discrete approximation. First, we describe properties of the standard l1, l2 and l∞ norms, and their essential characteristics for using as error criteria in discrete approximation. After that, we mention the possibility of applications of the so-called total least squares and total least lp norm, for finding the best approximation. Finally, we take...

In this paper, a general filter design norm is proposed with the intent of producing a unified design algorithm for all types of filters— FIR, IIR and 2-D FIR with complex specifications. The Chebyshev, least squares, and constrained least squares problems become special cases because this norm uses a convex combination of the 2-norm and the Chebyshev norm. The primary benefit of this new probl...

Fitted value iteration (FVI) with ordinary least squares regression is known to diverge. We present a new method, “Expansion-Constrained Ordinary Least Squares” (ECOLS), that produces a linear approximation but also guarantees convergence when used with FVI. To ensure convergence, we constrain the least squares regression operator to be a non-expansion in the∞-norm. We show that the space of fu...

We develop a linearly-constrained line-search adaptive filtering algorithm by incorporating the linear constraints into the least squares problem and searching the solution (filter weights) along the Kalman gain vector. The proposed algorithm performs close to the constrained recursive least squares (CRLS) algorithm while having a computational complexity comparable to the constrained least mea...

This paper focuses on total least squares (TLS) problems AX ≈ B with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnětynková, M. Plešinger, D. M. Sima, Z. Strakoš, and S. Van Huffel (2011)]. For TLS problems with single right-hand sides the paper [C. C. Paige and Z. Strakoš (2006)] showed how necessary and sufficient infor...

The contribution of our paper is to present a mixed finite element method for 4 estimation of the velocity in the optical flow constraint, i.e., an advection equation. The resulting 5 inverse problem is well-known to be undetermined because the velocity vector cannot be recovered 6 from the scalar field advected unless further restrictions on the flow, or motion are imposed. If 7 we suppose, fo...

The weighted low-rank approximation problem in general has no analytical solution in terms of the singular value decomposition and is solved numerically using optimization methods. Four representations of the rank constraint that turn the abstract problem formulation into parameter optimization problems are presented. The parameter optimization problem is partially solved analytically, which re...