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1.
We describe a procedure for determining a few of the largest singular values of a large sparse matrix. The method by Golub and Kent which uses the method of modified moments for estimating the eigenvalues of operators used in iterative methods for the solution of linear systems of equations is appropriately modified in order to generate a sequence of bidiagonal matrices whose singular values approximate those of the original sparse matrix. A simple Lanczos recursion is proposed for determining the corresponding left and right singular vectors. The potential asynchronous computation of the bidiagonal matrices using modified moments with the iterations of an adapted Chebyshev semi-iterative (CSI) method is an attractive feature for parallel computers. Comparisons in efficiency and accuracy with an appropriate Lanczos algorithm (with selective re-orthogonalization) are presented on large sparse (rectangular) matrices arising from applications such as information retrieval and seismic reflection tomography. This procedure is essentially motivated by the theory of moments and Gauss quadrature.This author's work was supported by the National Science Foundation under grants NSF CCR-8717492 and CCR-910000N (NCSA), the U.S. Department of Energy under grant DOE DE-FG02-85ER25001, and the Air Force Office of Scientific Research under grant AFOSR-90-0044 while at the University of Illinois at Urbana-Champaign Center for Supercomputing Research and Development.This author's work was supported by the U.S. Army Research Office under grant DAAL03-90-G-0105, and the National Science Foundation under grant NSF DCR-8412314. 相似文献
2.
We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2–4 matrix–vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices. 相似文献
3.
A. P. Golub 《Ukrainian Mathematical Journal》1989,41(6):690-694
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 6, pp. 803–808, June, 1989. 相似文献
4.
5.
Yurkshtovich N. K. Golub N. V. Kaputskii F. N. Yurkshtovich T. L. Kosterova R. I. 《Russian Journal of Applied Chemistry》2004,77(6):901-904
Sorption of Fe(III), Al(III), and Cr(III) on monocarboxy cellulose at various pH, concentrations of metal chloride or sulfate in solution, and time was studied. The effect of type and amount of the cation sorbed on the physicomechanical properties, swelling, and stability in phosphate buffer of monocarboxy cellulose fibers was considered. 相似文献
6.
Anionie Nickel Pseudohalide Complexes of the Types [Ni{N(CN)2}3]? and [Ni{N(CN)2}2(NCS)2]2? The preparation of a new type of anionic pseudohalide complexes of nickel [Ni{N(CN)2}3]? and of mixed thiocyanate-dicyanamide complexes [Ni{N(CN)2}2(NCS)2]2? is reported. The structures of the complexes are discussed on the basis of IR- and magnetic measurements. The new compounds are representing polymer octahedral complexes with a bridging function of the dicyanamide ligands. 相似文献
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8.
The differential excess enthalpy of mixed micelle formation was measured at different temperatures by mixing nonionic hexa(ethylene glycol) mono n-dodecyl ether with anionic sodium dodecyl sulfate or cationic dodecylpyridinium chloride. The experimental data were obtained calorimetrically by titrating a concentrated surfactant solution into a micellar solution of nonionic surfactant. The composition and the size of the mixed nonionic/ionic micelles at different surfactant concentrations were also determined. Pronounced differences in both composition and excess enthalpy were found between the anionic and the cationic mixed system. For both systems, the excess enthalpies become more exothermic with increasing temperature, but for the anionic mixed system an additional exothermic contribution was found which was much less temperature dependent. Temperature dependence of the excess enthalpy was attributed to the effect of the ionic headgroup on the hydration of the ethylene oxide (EO) groups in the mixed corona. Ionic headgroups located in the ethylene oxide layer cause the dehydration of the EO chains resulting in an additional hydrophobic contribution to the enthalpy of mixing. A high affinity of sodium dodecyl sulfate for nonionic micelles and an extra exothermic and less temperature dependent contribution to the excess enthalpy found for the SDS-C(12)E(6) system might be attributed to specific interactions (hydrogen bonds) between the sulfate headgroup and the partly dehydrated EO chain. 相似文献
9.
Lu Z Prouty MD Guo Z Golub VO Kumar CS Lvov YM 《Langmuir : the ACS journal of surfaces and colloids》2005,21(5):2042-2050
We explored using a magnetic field to modulate the permeability of polyelectrolyte microcapsules prepared by layer-by-layer self-assembly. Ferromagnetic gold-coated cobalt (Co@Au) nanoparticles (3 nm diameter) were embedded inside the capsule walls. The final 5 mum diameter microcapsules had wall structures consisting of 4 bilayers of poly(sodium styrene sulfonate)/poly(allylamine hydrochloride) (PSS/PAH), 1 layer of Co@Au, and 5 bilayers of PSS/PAH. External alternating magnetic fields of 100-300 Hz and 1200 Oe were applied to rotate the embedded Co@Au nanoparticles, which subsequently disturbed and distorted the capsule wall and drastically increased its permeability to macromolecules like FITC-labeled dextran. The capsule permeability change was estimated by taking the capsule interior and exterior fluorescent intensity ratio using confocal laser scanning microscopy. Capsules with 1 layer of Co@Au nanoparticles and 10 polyelectrolyte bilayers are optimal for magnetically controlling permeability. A theoretical explanation was proposed for the permeability control mechanisms. "Switching on" of these microcapsules using a magnetic field makes this method a good candidate for controlled drug delivery in biomedical applications. 相似文献
10.
Quadratically constrained least squares and quadratic problems 总被引:9,自引:0,他引:9
Summary We consider the following problem: Compute a vectorx such that Ax–b2=min, subject to the constraint x2=. A new approach to this problem based on Gauss quadrature is given. The method is especially well suited when the dimensions ofA are large and the matrix is sparse.It is also possible to extend this technique to a constrained quadratic form: For a symmetric matrixA we consider the minimization ofx
T
A
x–2b
T
x subject to the constraint x2=.Some numerical examples are given.This work was in part supported by the National Science Foundation under Grant DCR-8412314 and by the National Institute of Standards and Technology under Grant 60NANB9D0908. 相似文献