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Integral Methods in Science and Engineering pp 127–134Cite as

A System Iterative Method for Solving First-Kind, Degraded Identity Operator Equations

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Keywords

  • Gaussian Kernel
  • Point Spread Function
  • True Solution
  • Tikhonov Regularization
  • Feature Kernel

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References

  1. Groetsch, C.W.: The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind. Pitman, London (1977).

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  2. Hilgers, J.W., Bertram, B.S., Reynolds, W.R.: Use of cross-referencing for solving the parameter choice problem in generalized CLS. In: Schiavone, P., Constanda, C., Midouchowski, A. (eds.), Integral Methods in Scienc and Engineering. Birkhäuser, Boston (2002), pp. 105–110.

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  3. Hilgers, J.W., Bertram, B.S.: Comparing different types of approximators for choosing the parameters in the regularization of ill-posed problems. Computers Math. Appl., 48, 1779–1790 (2004).

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  4. Morozov, V.A.: Methods for Solving Incorrectly Posed Problems. Springer, Berlin-Heidelberg-New York (1984).

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  5. Tikhonov, A.N.: Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl. (1963), pp. 1035–1038.

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  6. Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. Winston, Washington, DC (1977).

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Author information

Authors and Affiliations

  1. Michigan Technological University, Houghton, MI, USA

    J. Hilgers & B. Bertram

  2. Signature Research Inc, Calumet, MI, USA

    J. Hilgers & W. Reynolds

Authors
  1. J. Hilgers
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  2. B. Bertram
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  3. W. Reynolds
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Editor information

Editors and Affiliations

  1. Department of Mathematical and Computer Sciences, University of Tulsa, 600 South College Avenue, Tulsa, OK 74104, USA

    C. Constanda

  2. Department of Civil and Environmental Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada

    S. Potapenko

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© 2008 Birkhäuser Boston

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Hilgers, J., Bertram, B., Reynolds, W. (2008). A System Iterative Method for Solving First-Kind, Degraded Identity Operator Equations. In: Constanda, C., Potapenko, S. (eds) Integral Methods in Science and Engineering. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4671-4_15

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