메뉴 건너뛰기




Volumn 58, Issue 5, 2008, Pages 726-741

Recovery of functions from weak data using unsymmetric meshless kernel-based methods

Author keywords

Approximation; Convolution; Error bounds; Least squares; Overdetermined systems; Petrov Galerkin; Stability

Indexed keywords

ERROR ANALYSIS; FUNCTION EVALUATION; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL TECHNIQUES;

EID: 41149167279     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2007.02.009     Document Type: Article
Times cited : (6)

References (28)
  • 3
    • 0032136132 scopus 로고    scopus 로고
    • A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
    • Atluri S.N., and Zhu T.L. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22 (1998) 117-127
    • (1998) Comput. Mech. , vol.22 , pp. 117-127
    • Atluri, S.N.1    Zhu, T.L.2
  • 6
    • 0035120922 scopus 로고    scopus 로고
    • A stabilized conforming nodal integration for Galerkin mesh-free methods
    • Chen J.S., Wu C.T., Yoon S., and You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. Int. J. Numer. Methods Engrg. 50 (2001) 435-466
    • (2001) Int. J. Numer. Methods Engrg. , vol.50 , pp. 435-466
    • Chen, J.S.1    Wu, C.T.2    Yoon, S.3    You, Y.4
  • 7
    • 8544220284 scopus 로고
    • Basic error estimates for elliptic problems
    • Ciarlet P.G., and Lions J.-L. (Eds), North-Holland, Amsterdam
    • Ciarlet P.G. Basic error estimates for elliptic problems. In: Ciarlet P.G., and Lions J.-L. (Eds). Handbook of Numerical Analysis vol. 2 (1991), North-Holland, Amsterdam 17-351
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 17-351
    • Ciarlet, P.G.1
  • 8
    • 0032624422 scopus 로고    scopus 로고
    • Numerical integration of the Galerkin weak form in meshfree methods
    • Dolbow J., and Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods. Comput. Mech. 23 3 (1999) 219-230
    • (1999) Comput. Mech. , vol.23 , Issue.3 , pp. 219-230
    • Dolbow, J.1    Belytschko, T.2
  • 9
    • 0037988444 scopus 로고
    • Studies of the r parameter in the multiquadric function applied to ground water pumping
    • Hagan R.E., and Kansa E.J. Studies of the r parameter in the multiquadric function applied to ground water pumping. J. Appl. Sci. Comput. 1 (1994) 266-281
    • (1994) J. Appl. Sci. Comput. , vol.1 , pp. 266-281
    • Hagan, R.E.1    Kansa, E.J.2
  • 10
    • 41149148751 scopus 로고    scopus 로고
    • E.J. Kansa, Application of Hardy's multiquadric interpolation to hydrodynamics, in: Proc. 1986 Simul. Conf., vol. 4, 1986, pp. 111-117
    • E.J. Kansa, Application of Hardy's multiquadric interpolation to hydrodynamics, in: Proc. 1986 Simul. Conf., vol. 4, 1986, pp. 111-117
  • 11
    • 41149170807 scopus 로고    scopus 로고
    • L. Ling, R. Schaback, Stable and convergent unsymmetric meshless collocation methods, Preprint, 2006
    • L. Ling, R. Schaback, Stable and convergent unsymmetric meshless collocation methods, Preprint, 2006
  • 12
    • 33748967993 scopus 로고    scopus 로고
    • An estimate for multivariate interpolation II
    • Madych W. An estimate for multivariate interpolation II. J. Approx. Theory 142 (2006) 116-128
    • (2006) J. Approx. Theory , vol.142 , pp. 116-128
    • Madych, W.1
  • 13
    • 0001868023 scopus 로고
    • Approximate approximations
    • Whiteman J.R. (Ed), John Wiley and Sons, Chichester
    • Maz'ya V. Approximate approximations. In: Whiteman J.R. (Ed). The Mathematics of Finite Elements and Applications (1994), John Wiley and Sons, Chichester 77-104
    • (1994) The Mathematics of Finite Elements and Applications , pp. 77-104
    • Maz'ya, V.1
  • 14
    • 33745292987 scopus 로고    scopus 로고
    • Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions
    • Narcowich F.J., Ward J.D., and Wendland H. Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions. Constructive Approximation 24 (2006) 175-186
    • (2006) Constructive Approximation , vol.24 , pp. 175-186
    • Narcowich, F.J.1    Ward, J.D.2    Wendland, H.3
  • 15
    • 33646732403 scopus 로고    scopus 로고
    • Multiscale kernels
    • Opfer R. Multiscale kernels. Adv. Comput. Math. 25 4 (2006) 357-380
    • (2006) Adv. Comput. Math. , vol.25 , Issue.4 , pp. 357-380
    • Opfer, R.1
  • 16
    • 0000190592 scopus 로고    scopus 로고
    • Native Hilbert spaces for radial basis functions I
    • Buhmann M.D., Mache D.H., Felten M., and Müller M.W. (Eds), Birkhäuser, Basel
    • Schaback R. Native Hilbert spaces for radial basis functions I. In: Buhmann M.D., Mache D.H., Felten M., and Müller M.W. (Eds). New Developments in Approximation Theory, International Series of Numerical Mathematics vol. 132 (1999), Birkhäuser, Basel 255-282
    • (1999) New Developments in Approximation Theory, International Series of Numerical Mathematics , vol.132 , pp. 255-282
    • Schaback, R.1
  • 17
    • 0034274841 scopus 로고    scopus 로고
    • A unified theory of radial basis functions (Native Hilbert spaces for radial basis functions II)
    • Schaback R. A unified theory of radial basis functions (Native Hilbert spaces for radial basis functions II). J. Comp. Appl. Math. 121 (2000) 165-177
    • (2000) J. Comp. Appl. Math. , vol.121 , pp. 165-177
    • Schaback, R.1
  • 18
    • 40049104874 scopus 로고    scopus 로고
    • Convergence of unsymmetric kernel-based meshless collocation methods
    • Schaback R. Convergence of unsymmetric kernel-based meshless collocation methods. SIAM J. Numer. Anal. 45 (2007) 333-351
    • (2007) SIAM J. Numer. Anal. , vol.45 , pp. 333-351
    • Schaback, R.1
  • 19
    • 41149139505 scopus 로고    scopus 로고
    • R. Schaback, Unsymmetric meshless methods for operator equations, Preprint, Göttingen, 2006
    • R. Schaback, Unsymmetric meshless methods for operator equations, Preprint, Göttingen, 2006
  • 20
    • 41149090827 scopus 로고    scopus 로고
    • R. Schaback, Why Does MLPG Work? Accepted paper for a keynote lecture in ICCES 07, Göttingen, 2006
    • R. Schaback, Why Does MLPG Work? Accepted paper for a keynote lecture in ICCES 07, Göttingen, 2006
  • 21
    • 0036013533 scopus 로고    scopus 로고
    • Inverse and saturation theorems for radial basis function interpolation
    • Schaback R., and Wendland H. Inverse and saturation theorems for radial basis function interpolation. Math. Comp. 71 238 (2002) 669-681
    • (2002) Math. Comp. , vol.71 , Issue.238 , pp. 669-681
    • Schaback, R.1    Wendland, H.2
  • 22
    • 33646731541 scopus 로고    scopus 로고
    • Kernel techniques: From machine learning to meshless methods
    • Schaback R., and Wendland H. Kernel techniques: From machine learning to meshless methods. Acta Numer. 15 (2006) 543-639
    • (2006) Acta Numer. , vol.15 , pp. 543-639
    • Schaback, R.1    Wendland, H.2
  • 23
    • 0346847275 scopus 로고
    • Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
    • Wendland H. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math. 4 (1995) 389-396
    • (1995) Adv. Comput. Math. , vol.4 , pp. 389-396
    • Wendland, H.1
  • 25
    • 26644433217 scopus 로고    scopus 로고
    • Approximate interpolation with applications to selecting smoothing parameters
    • Wendland H., and Rieger C. Approximate interpolation with applications to selecting smoothing parameters. Numer. Math. 101 (2005) 729-748
    • (2005) Numer. Math. , vol.101 , pp. 729-748
    • Wendland, H.1    Rieger, C.2
  • 26
    • 41149088367 scopus 로고    scopus 로고
    • The role of the multiquadric shape parameters in solving elliptic partial differential equations
    • Wertz J., Kansa E.J., and Ling L. The role of the multiquadric shape parameters in solving elliptic partial differential equations. Comput. Math. Appl. 51 8 (2004) 1135-1140
    • (2004) Comput. Math. Appl. , vol.51 , Issue.8 , pp. 1135-1140
    • Wertz, J.1    Kansa, E.J.2    Ling, L.3
  • 27
    • 51649133223 scopus 로고
    • Hermite-Birkhoff interpolation of scattered data by radial basis functions
    • Wu Z. Hermite-Birkhoff interpolation of scattered data by radial basis functions. Approx. Theory Appl. 8 (1992) 1-10
    • (1992) Approx. Theory Appl. , vol.8 , pp. 1-10
    • Wu, Z.1
  • 28
    • 0000136089 scopus 로고
    • Multivariate compactly supported positive definite radial functions
    • Wu Z. Multivariate compactly supported positive definite radial functions. Adv. Comput. Math. 4 (1995) 283-292
    • (1995) Adv. Comput. Math. , vol.4 , pp. 283-292
    • Wu, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.