APM  Vol.5 No.14 , December 2015
Matrices Associated with Moving Least-Squares Approximation and Corresponding Inequalities
ABSTRACT
In this article, some properties of matrices of moving least-squares approximation have been proven. The used technique is based on known inequalities for singular-values of matrices. Some inequalities for the norm of coefficients-vector of the linear approximation have been proven.

Cite this paper
Nenov, S. and Tsvetkov, T. (2015) Matrices Associated with Moving Least-Squares Approximation and Corresponding Inequalities. Advances in Pure Mathematics, 5, 856-864. doi: 10.4236/apm.2015.514080.
References
[1]   Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D. and Silva, C.T. Point-Set Surfaces.
http://www.math.tau.ac.il/~levin/

[2]   Levin, D. The Approximation Power of Moving Least-Squares.
http://www.math.tau.ac.il/~levin/

[3]   Levin, D. Mesh-Independent Surface Interpolation.
http://www.math.tau.ac.il/~levin/

[4]   Levin, D. (1999) Stable Integration Rules with Scattered Integration Points. Journal of Computational and Applied Mathematics, 112, 181-187.
http://www.math.tau.ac.il/~levin/
http://dx.doi.org/10.1016/S0377-0427(99)00218-6


[5]   Fasshauer, G. (2003) Multivariate Meshfree Approximation.
http://www.math.iit.edu/~fass/603_ch7.pdf

[6]   Lu, L.-Z. and Pearce, C.E.M. (2000) Some New Bounds for Singular Values and Eigenvalues of Matrix Products. Annals of Operations Research, 98, 141-148.
http://dx.doi.org/10.1023/A:1019200322441

[7]   Merikoski, J.K. (2004) Ravinder Kumar, Inequalities for Spreads of Matrix Sums and Products. Applied Mathematics E-Notes, 4, 150-159.

[8]   Jabbari, F. (2015) Linear System Theory II. Chapter 3: Eigenvalue, Singular Values, Pseudo-Inverse. The Henry Samueli School of Engineering, University of California, Irvine.
http://gram.eng.uci.edu/~fjabbari/me270b/me270b.html

[9]   Hartman, P. (2002) Ordinary Differential Equations. Second Edition, SIAM, Philadelphia, Pennsylvania, United States.
http://dx.doi.org/10.1137/1.9780898719222.fm

 
 
Top