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941.
Jean-Claude Yakoubsohn 《Numerical Algorithms》1995,9(2):223-244
We give a new theorem concerning the convergence of Newton's method to compute an approximate zero of a system of equations. In this result, the constanth
0=0.162434... appears, which plays a fundamental role in the localization of good initial points for the Newton iteration. We apply it to the determination of an appropriate discretization of the time interval in the classical homotopy method. 相似文献
942.
Xiaopu Yan 《Numerical Algorithms》1995,10(2):245-260
Multistep methods for the differential/algebraic equations (DAEs) in the form of
相似文献
943.
Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution
belongs to the range of the operator (T
*
T)
v
, o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India. 相似文献
944.
A highly sensitive and selective fluorescence-quenching kinetic method is proposed for the determination of trace osmium(IV), based on the catalytic effect of osmium(IV) on the salicylfluorone (ex = 510 nm, em = 535 nm)-H2O2 system at pH 9.3–9.6. Using the fixed time method, osmium(IV) in the range 0.008–0.6 ng/ml can be determined. The detection limit is 0.006 ng/ml. Over thirty anions and cations, including other platinum metal ions, do not interfere, even when present in large excess. The method has been applied successfully for the determination of osmium in a series of synthetic mixtures and refined ore with relative standard deviations of 2–6%. 相似文献
945.
On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds 总被引:11,自引:0,他引:11
We consider a new algorithm, an interior-reflective Newton approach, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection paths). The interior-reflective approach does not require identification of an activity set. In this paper we establish that the interior-reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interior-reflective Newton methods which can be used for large-scale and sparse problems.Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-86ER25013.A000, and in part by NSF, AFOSR, and ONR through grant DMS-8920550, and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.Corresponding author. 相似文献
946.
Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037. 相似文献
947.
948.
949.
Let be complex numbers, and consider the power sums , . Put , where the minimum is over all possible complex numbers satisfying the above. Turán conjectured that , for some positive absolute constant. Atkinson proved this conjecture by showing . It is now known that , for . Determining whether or approaches some other limiting value as is still an open problem. Our calculations show that an upper bound for decreases for , suggesting that decreases to a limiting value less than as .
950.
For the multidimensional heat equation in a parallelepiped, optimal error estimates inL
2(Q) are derived. The error is of the order of +¦h¦2 for any right-hand sidef L
2(Q) and any initial function
; for appropriate classes of less regularf andu
0, the error is of the order of ((+¦h¦2
), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996. 相似文献
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