In this paper, a model identification method for the unknown environments has been developed. By the interactions between a mobile manipulator and the unknown object, a nonholonomic cart, the sensory information has been collected to estimate the model parameters of the cart, which are used to control the cart. Since the raw data are contaminated by noise that can not be modeled statistically, ...

Starting from the residual estimates for GMRES formulated by many authors, usually in terms of the quotient of the Hermitian part and the norm of a matrix or by using the field of values of a matrix, we present more general estimates which hold also for restarted and augmented GMRES. Sufficient conditions for convergence are formulated. All estimates are independent on the choice of an initial ...

We study an interior-point gradient method for solving a class of so-called totally nonnegative least squares problems. At each iteration, the method decreases the residual norm along a diagonally scaled negative gradient direction with a special scaling. We establish the global convergence of the method, and present some numerical examples to compare the proposed method with a few similar meth...

The standard approaches to solving overdetermined linear systems Bx ≈ c construct minimal corrections to the data to make the corrected system compatible. In ordinary least squares (LS) the correction is restricted to the right hand side c, while in scaled total least squares (STLS) [14, 12] corrections to both c and B are allowed, and their relative sizes are determined by a real positive para...

Minimum residual norm iterative methods for solving linear systems Ax = b can be viewed as, and are often implemented as, sequences of least squares problems involving Krylov subspaces of increasing dimensions. The minimum residual method (MINRES) [C. Paige and M. Saunders, SIAM J. Numer. Anal., 12 (1975), pp. 617–629] and generalized minimum residual method (GMRES) [Y. Saad and M. Schultz, SIA...

and Kk(BA,Br) = span{Br, (BA)Br, . . . , (BA)k−1Br}, (3) where B ∈ Rn×m is the mapping and preconditioning matrix, and apply Krylov subspace iteration methods on these subspaces. For overdetermined problems, applying the standard CG method to Kk(BA,Br) leads to the preconditioned CGLS [3] or CGNR [9] method while for underdetermined problems it leads to preconditioned CGNE [9] method. The GMRES...