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...

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 least-squares method can be used to approximate an eigenvector for a matrix when only an approximation is known for the corresponding eigenvalue. In this paper, this technique is analyzed and error estimates are established proving that if the error in the eigenvalue is sufficiently small, then the error in the approximate eigenvector produced by the least-squares method is also small. Also...

| We present simple exponential approximations to the transient behavior of the stable M=M=1 queue. The approximations are optimal in a least-squares sense, and we nd them to agree well with exact results. Our approach can be used to derive approximations for any time-dependent quantity with a known Laplace transform, e.g., the probability distribution and the moments of the queue size, of the ...

The consistency and asymptotic normality of a linear least squares estimate of the form (X,X)-X’Y when the mean is not X/I is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not ...

Abstract. 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 a necessary and suff...

Abstrucf-Developments in the theory of linear least-squares estimation in the last thirty years or so are outlined. Particular attention is paid to early mathematical. wurk in the field and to more modem developments showing some of the many connections between least-squares filtering and other fields.

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 ...

In a recent paper of the author [A. Sidi, A new approach to vector-valued rational interpolation, J. Approx. Theory 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where F : C → CN , were proposed, and some of their algebraic properties were studied. One of these procedures, denoted IMPE, was defined via the solution of a linear least-squares problem. I...