共查询到10条相似文献,搜索用时 444 毫秒
1.
The paper reviews studies on the representations and expansions of weighted pseudoinverse matrices with positive definite
weights and on iterative methods and regularized problems for calculation of weighted pseudoinverse matrices and weighted
normal pseudosolutions. The use of these methods to solve constrained least-squares problems is examined.
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 47–73, January–February 2008. 相似文献
2.
Weighted pseudoinverse matrices with positive definite weights are expanded into matrix power products with negative exponents
and arbitrary positive parameters. These expansions are used to develop and analyze iterative methods for evaluating weighted
pseudoinverse matrices and weighted normal pseudosolutions and solving constrained least-squares problems.
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 45–64, January–February 2007. 相似文献
3.
Three iterative processes are constructed and investigated for computing weighted pseudoinverse matrices with singular weights
and ML-weighted pseudoinverse matrices. Two of them are based on the decompositions of the weighted pseudoinverse matrix with
singular weights into matrix power series, and the third is a generalization of the Schulz method to nonsingular square matrices.
Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 150–169, September–October, 1999. 相似文献
4.
Weighted pseudoinverse matrices are expanded into matrix power series with negative exponents and arbitrary positive parameters.
Based on this expansion, iterative methods for evaluating weighted pseudoinverse matrices and weighted normal pseudosolutions
are designed and analyzed. The iterative methods for weighted normal pseudosolutions are extended to solving constrained least-squares
problems.
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 32–62, January–February 2006. 相似文献
5.
Limiting Representations of Weighted Pseudoinverse Matrices with Positive Definite Weights. Problem Regularization 总被引:2,自引:2,他引:0
Limiting representations for weighted pseudoinverse matrices with positive definite weights are derived. It is shown that regularized problems can be constructed based on such limiting representations intended for evaluation of weighted pseudoinverse matrices and weighted normal pseudosolutions with positive definite weights. The results obtained, concerning regularization of problems on evaluation of weighted normal pseudosolutions, are employed for regularization of least-squares problems with constraints. 相似文献
6.
A weighted least squares problem {ie863-01} with positive definite weights M and N is considered, where A ∈ Rm×n is a rank-deficient matrix, b ∈ Rm. The hereditary, computational, and global errors of a weighted normal pseudosolution are estimated for perturbed initial
data, including the case where the rank of the perturbed matrix varies.
Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 83–95, November–December 2008. 相似文献
7.
In this paper, we study formally high-order accurate discontinuous Galerkin methods on general arbitrary grid for multi-dimensional
hyperbolic systems of conservation laws [Cockburn, B., and Shu, C.-W. (1989, Math. Comput. 52, 411–435, 1998, J. Comput. Phys. 141, 199–224); Cockburn et al. (1989, J. Comput. Phys. 84, 90–113; 1990, Math. Comput. 54, 545–581). We extend the notion of E-flux [Osher (1985) SIAM J. Numer. Anal. 22, 947–961] from scalar to system, and found that after flux splitting upwind flux [Cockburn et al. (1989) J. Comput. Phys. 84, 90–113] is a Riemann solver free E-flux for systems. Therefore, we are able to show that the discontinuous Galerkin methods
satisfy a cell entropy inequality for square entropy (in semidiscrete sense) if the multi-dimensional systems are symmetric.
Similar result [Jiang and Shu (1994) Math. Comput. 62, 531–538] was obtained for scalar equations in multi-dimensions. We also developed a second-order finite difference version
of the discontinuous Galerkin methods. Numerical experiments have been obtained with excellent results.
相似文献
8.
9.
A New Smoothness Indicator for the WENO Schemes and Its Effect on the Convergence to Steady State Solutions 总被引:1,自引:0,他引:1
The convergence to steady state solutions of the Euler equations for the fifth-order weighted essentially non-oscillatory
(WENO) finite difference scheme with the Lax–Friedrichs flux splitting [7, (1996) J. Comput. Phys. 126, 202–228.] is studied through systematic numerical tests. Numerical evidence indicates that this type of WENO scheme suffers
from slight post-shock oscillations. Even though these oscillations are small in magnitude and do not affect the “essentially
non-oscillatory” property of WENO schemes, they are indeed responsible for the numerical residue to hang at the truncation
error level of the scheme instead of settling down to machine zero. We propose a new smoothness indicator for the WENO schemes
in steady state calculations, which performs better near the steady shock region than the original smoothness indicator in
[7, (1996) J. Comput. Phys. 126, 202–228.]. With our new smoothness indicator, the slight post-shock oscillations are either removed or significantly reduced
and convergence is improved significantly. Numerical experiments show that the residue for the WENO scheme with this new smoothness
indicator can converge to machine zero for one and two dimensional (2D) steady problems with strong shock waves when there
are no shocks passing through the domain boundaries.
Dedicated to the memory of Professor Xu-Dong Liu. 相似文献
10.
The numerical investigation of a recent family of algebraic fractional-step methods (the so called Yosida methods) for the solution of the incompressible time-dependent Navier–Stokes equations is presented. A comparison with the Karniadakis–Israeli–Orszag method Karniadakis et al. (1991, J. Comput. Phys. 97, 414–443) is carried out. The high accuracy in time of these schemes well combines with the high accuracy in space of spectral methods. 相似文献