Numerical solution for eigenvalues and eigenfunctions of a Hermitian kernel and an error estimate

Rakotch, E.

doi:10.1090/S0025-5718-1975-0373356-X

Numerical solution for eigenvalues and eigenfunctions of a Hermitian kernel and an error estimate
HTML articles powered by AMS MathViewer

by E. Rakotch PDF

Math. Comp. 29 (1975), 794-805 Request permission

Abstract:

New error estimates for eigenvalues of symmetric integral equations are obtained. These estimates are applicable to a more general class of integration methods and, in many cases, are better than those of Wielandt. For every eigenvalue, a numerical solution for the corresponding eigenfunction is also obtained. Whenever the exact eigenvalue happens to be simple, an error estimate for the corresponding eigenfunction is also derived.

References

Kendall E. Atkinson, The numerical solutions of the eigenvalue problem for compact integral operators, Trans. Amer. Math. Soc. 129 (1967), 458–465. MR 220105, DOI 10.1090/S0002-9947-1967-0220105-3
Christopher T. H. Baker, The deferred approach to the limit for eigenvalues of integral equations, SIAM J. Numer. Anal. 8 (1971), 1–10. MR 324927, DOI 10.1137/0708001
Helmut Brakhage, Zur Fehlerabschätzung für die numerische Eigenwertbestimmung bei Integralgleichungen, Numer. Math. 3 (1961), 174–179 (German). MR 129148, DOI 10.1007/BF01386016
Peter Linz, On the numerical computation of eigenvalues and eigenvectors of symmetric integral equations, Math. Comp. 24 (1970), 905–910. MR 275708, DOI 10.1090/S0025-5718-1970-0275708-0
S. G. Mihlin, Lektsii po lineĭ nym integral′nym uravneniyam, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1959 (Russian). MR 0123161
E. Rakotch, Numerical solution for eigenvalues and eigenfunctions of a Hermitian kernel and an error estimate, Math. Comput. 29 (1975), 794–805. MR 0373356, DOI 10.1090/S0025-5718-1975-0373356-X
John Todd, Introduction to the constructive theory of functions, Academic Press, Inc., New York, 1963. MR 0156129
Hermann Weyl, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung), Math. Ann. 71 (1912), no. 4, 441–479 (German). MR 1511670, DOI 10.1007/BF01456804
Helmut Wielandt, Error bounds for eigenvalues of symmetric integral equations, Proceedings of Symposia in Applied Mathematics. Vol. VI. Numerical analysis, McGraw-Hill Book Company, Inc., New York, for the American Mathematical Society, Providence, R.I., 1956, pp. 261–282. MR 0086402