Publication Cover
Applicable Analysis
An International Journal
Volume 6, 1976 - Issue 1
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Original Articles

Some projection methods for the eigenvalue problem

Pages 61-73 | Published online: 02 May 2007

References

  • Andrew , A.L. 1970 . Convergence of approximate operator methods for eigenvectors . Bull, Aust. Math. Soc. , 3 : 199 – 205 .
  • Birkhoff , G. , deBoor , C. , Swartz , B. and Wendroff , B. 1966 . Rayleigh-Ritz approximations by piecewise cubic polynomials . SI AM J. Numer. Anal. , 3 : 188 – 203 .
  • deBoor , C. 1966 . The method of projections as applied to the numerical solution of two point boundary value problems using cubic splines , Ann Arbor : Doctoral thesis, University of Michigan .
  • deBoor , C. 1968 . On uniform approximation by splines . J. Approximation Theory , 1 : 219 – 235 .
  • Fix , G. 1969 . Higher-order Rayleigh-Ritz approximations . J. Math. Mech. , 18 : 645 – 658 .
  • Fix , G. and Strang , G. 1969 . A Fourier analysis of the finite element variational method . 18
  • Kantorovich , L.V. and Akilov , G.P. 1964 . Functional Analysis in Normed Spaces , New York : Pergamon Press .
  • Lucas , T.R. and Reddien , G. 1972 . Some collocation methods for nonlinear boundary value problems . SI AM J. Numer. Anal. , 9 : 341 – 356 .
  • Nitsche , J. 1968 . Ein kriterium fur die quasi-optimalitae des Ritzschen verfahrens . Numer. Math. , 11 : 346 – 348 .
  • Phillips , J.L. 1972 . The use of collocation as a projection method for solving linear operator equations . SI AM J. Numer. Anal. , 9 : 14 – 28 .
  • Pierce , J.G. and Varga , R.S. 1972 . Higher order convergence rates for the Rayleigh-Ritz method applied to eigenvalue problems. I. Estimates relating Rayleigh-Ritz and Galerkin approximations to eigenfunctions . SIAM J. Numer.Anal. , 9 : 137 – 151 .
  • Pierce , J.G. and Varga , R.S. II. Error bounds for Rayleigh-Ritz approximations to eigenvalues
  • Putnam , C.R. 1967 . Perturbations of bounded operators . Niew Archief voor Wiskunde , XV : 146 – 152 .
  • Schultz , M.H. and Varga , R.S. 1967 . L-splines . Numer.Math. , 10 : 345 – 369 .
  • Schultz , M.H. 1969 . E-multivariate approximation theory . SIAM J.Numer.Anal. , 6 : 161 – 183 .
  • Schultz , M.H. 1969 . L2-approximation theory of even order multivariate splines . SIAM J.Numer.Anal. , 6 : 467 – 475 .
  • Vainikko , G.M. 1967 . On the speed of convergence of approximate methods in the eigenvalue problem . USSR Comp.Math.and Math.Phys. , 7 : 977 – 987 .

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