Skip to main content
SpringerLink
Log in

Eigenwertprobleme

  • Chapter
Numerische Mathematik 2

Part of the book series: Springer-Lehrbuch ((SLB))

  • 4965 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur zu Kapitel 6

  • Barth, W., Martin, R. S., Wilkinson, J. H. (1971): Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection. Contribution II/5 in Wilkinson and Reinsch (1971).

    Google Scholar 

  • Bauer, F. L., Fike, C. T. (1960): Norms and exclusion theorems. Numer. Math. 2, 137–141.

    MathSciNet  Google Scholar 

  • —, Stoer, J., Witzgall, C. (1961): Absolute and monotonic norms. Numer. Math. 3, 257–264.

    Article  MathSciNet  Google Scholar 

  • Bowdler, H., Martin, R. S., Wilkinson, J. H. (1971): The QR and QL algorithms for symmetric matrices. Contribution II/3 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • Bunse, W., Bunse-Gerstner, A. (1985): Numerische Lineare Algebra. Stuttgart: Teubner.

    Google Scholar 

  • Cullum, J., Willoughby, R. A. (1985): Lanczos Algorithms for Large Symmetric Eigenvalue Computations. Vol. I: Theory, Vol. II: Programs. Progress in Scientific Computing, Vol. 3, 4. Basel: Birkhäuser.

    Google Scholar 

  • Eberlein, P. J. (1971): Solution to the complex eigenproblem by a norm reducing Jacobi type method. Contribution II/17 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • Francis, J. F. G. (1961/62): The QR transformation. A unitary analogue to the LR transformation. I. Computer J. 4, 265–271. The QR transformation. II. ibid., 332–345.

    Article  MATH  MathSciNet  Google Scholar 

  • Garbow, B. S., et al. (1977): Matrix Eigensystem Computer Routines — EISPACK Guide Extension. Lecture Notes in Computer Science 51. Berlin, Heidelberg, New York: Springer-Verlag.

    Google Scholar 

  • Givens, J. W. (1954): Numerical computation of the characteristic values of a real symmetric matrix. Oak Ridge National Laboratory Report ORNL-1574.

    Google Scholar 

  • Golub, G. H., Reinsch, C. (1971): Singular value decomposition and least squares solution. Contribution I/10 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • —, Van Loan, C. F. (1983): Matrix Computations. Baltimore: The Johns-Hopkins University Press.

    Google Scholar 

  • —, Wilkinson, J. H. (1976): Ill-conditioned eigensystems and the computation of the Jordan canonical form. SIAM Review 18, 578–619.

    MATH  MathSciNet  Google Scholar 

  • Householder, A. S. (1964): The Theory of Matrices in Numerical Analysis. New York: Blaisdell.

    Google Scholar 

  • Kaniel, S. (1966): Estimates for some computational techniques in linear algebra. Math. Comp. 20, 369–378.

    MATH  MathSciNet  Google Scholar 

  • Kie lbasinski, A., Schwetlick, H. (1988): Numerische Lineare Algebra. Thun, Frankfurt/M.: Deutsch.

    Google Scholar 

  • Kublanovskaya, V. N. (1961): On some algorithms for the solution of the complete eigenvalue problem. Ž. Vyčisl. Mat. i Mat. Fiz. 1, 555–570.

    MATH  Google Scholar 

  • Lanczos, C. (1950): An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Stand. 45, 255–282.

    MathSciNet  Google Scholar 

  • Martin, R. S., Peters, G., Wilkinson, J. H. (1971): The QR algorithm for real Hessenberg matrices. Contribution II/14 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • —, Reinsch, C., Wilkinson. J. H. (1971): Householder's tridiagonalization of a symmetric matrix. Contribution II/2 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • —, Wilkinson, J. H. (1971): Reduction of the symmetric eigenproblem Ax = λBx and related problems to standard form. Contribution II/10 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • —, Wilkinson, J. H. (1971): Similarity reduction of a general matrix to Hessenberg form. Contribution II/13 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • Moler, C. B., Stewart, G. W. (1973): An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10, 241–256.

    Article  MathSciNet  Google Scholar 

  • Paige, C. C. (1971): The computation of eigenvalues and eigenvectors of very large sparse matrices. Ph.D. thesis, London University.

    Google Scholar 

  • Parlett, B. N. (1965): Convergence of the QR algorithm. Numer. Math. 7, 187–193 (korr. in 10, 163–164 (1967)).

    Article  MATH  MathSciNet  Google Scholar 

  • Parlett, B. N. (1980): The Symmetric Eigenvalue Problem. Englewood Cliffs, N.J.: Prentice-Hall.

    Google Scholar 

  • —, Poole, W. G. (1973): A geometric theory for the QR, LU and power iterations. SIAM J. Numer. Anal. 10, 389–412.

    MATH  MathSciNet  Google Scholar 

  • —, Scott, D. S. (1979): The Lanczos algorithm with selective orthogonalization. Math Comp. 33, 217–238.

    MATH  MathSciNet  Google Scholar 

  • Peters, G., Wilkinson J. H. (1970): Ax = λBx and the generalized eigenproblem. SIAM J. Numer. Anal. 7, 479–492.

    Article  MathSciNet  Google Scholar 

  • —, — (1971): Eigenvectors of real and complex matrices by LR and QR triangularizations. Contribution II/15 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • —, — (1971): The calculation of specified eigenvectors by inverse iteration. Contribution II/18 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • Rutishauser, H. (1958): Solution of eigenvalue problems with the LR-transformation. Nat. Bur. Standards Appl. Math. Ser. 49, 47–81.

    MATH  MathSciNet  Google Scholar 

  • — (1971): The Jacobi method for real symmetric matrices. Contribution II/1 in: Wilkinson and Reinsch (1971).

    Google Scholar 

  • Saad, Y. (1980): On the rates of convergence of the Lanczos and the block Lanczos methods. SIAM J. Num. Anal. 17, 687–706.

    MATH  MathSciNet  Google Scholar 

  • Schwarz, H. R., Rutishauser, H., Stiefel, E. (1972): Numerik symmetrischer Matrizen. 2d ed. Stuttgart: Teubner. (Englische Übersetzung: Englewood Cliffs, N.J.: Prentice-Hall (1973).)

    Google Scholar 

  • Smith, B. T., et al. (1976): Matrix eigensystems routines — EISPACK Guide. Lecture Notes in Computer Science 6, 2d ed. Berlin, Heidelberg, New York: Springer-Verlag.

    Google Scholar 

  • Stewart, G. W. (1973): Introduction to Matrix Computations. New York, London: Academic Press.

    Google Scholar 

  • Wilkinson, J. H. (1962): Note on the quadratic convergence of the cyclic Jacobi process. Numer. Math. 4, 296–300.

    MATH  MathSciNet  Google Scholar 

  • — (1965): The Algebraic Eigenvalue Problem. Oxford: Clarendon Press.

    Google Scholar 

  • — (1968): Global convergence of tridiagonal QR algorithm with origin shifts. Linear Algebra and Appl. 1, 409–420.

    MathSciNet  Google Scholar 

  • —, Reinsch, C. (1971): Linear Algebra, Handbook for Automatic Computation, Vol. II. Berlin, Heidelberg, New York: Springer-Verlag.

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2005). Eigenwertprobleme. In: Numerische Mathematik 2. Springer-Lehrbuch. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26268-7_1

Download citation

Publish with us

Policies and ethics

Search

Navigation