The matrix-form LSQR method is presented in this paper for solving the least squares problem of the matrix equation AXB = C with tridiagonal matrix constraint. Based on a matrix-form bidiagonalization procedure, the least squares problem associated with the tridiagonal constrained matrix equation AXB = C reduces to a unconstrained least squares problem of linear system, which can be solved by u...

We discretise the Lax pair for reduced Nahm systems and prove its equivalence with Kahan–Hirota–Kimura discretisation procedure. show that these pairs guarantee integrability of discrete providing an invariant. Also, we cannot solve general problem characterisation discretisations.

The main purpose of this paper is to show that linear least squares methods based on bidiagonalization, namely the LSQR algorithm, can be used for generation of trust region path. This property is a basis for an inexact trust region method which uses the LSQR algorithm for direction determination. This method is very efficient for large sparse nonlinear least squares as it is supported by numer...

We perform an analytic and experimental study of line iterative methods for solving linear systems arising from finite difference discretizations of non-self-adjoint elliptic partial differential equations on two-dimensional domains. The methods consist of performing one step of cyclic reduction, followed by solution of the resulting reduced system by line relaxation. We augment previous analys...

Area-Under-the-Concentration Curve, Bruce Kaplan,* Herwig-Ulf Meier-Kriesche, Kimberly Napoli, and Barry D. Kahan (Div. of Renal Dis. and Hypertension, Dept. of Internal Med., and Div. of Immunol. and Organ Transplant., Dept. of Surgery, The University of Texas Medical School at Houston, 6431 Fannin, Suite 4.163, Houston, TX 77030; *author for correspondence and reprint requests: fax 713-794-1197)

A version of the Davis-Kahan Tan 2Θ theorem [SIAM J. Numer. Anal. 7 (1970), 1 – 46] for not necessarily semibounded linear operators defined by quadratic forms is proven. This theorem generalizes a recent result by Motovilov and Selin [Integr. Equat. Oper. Theory 56 (2006), 511 – 542].

Subjects gave magnitude estimates of the loudness of monaurally presented pure tones (1000, 1040, and 1080 Hz) and dichotically presented pairs of tones (1000 Hz to one ear plus 1040 or 1080 Hz to the other). For each monaural frequency or dichotic pair, the magnitude estimates approximated power functions of sound pressure; moreover, the monaural and dichotic loudness functions were separated ...