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Consistency of the Tikhonov's regularization in an ill-posed problem with random data

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  • Dahmani, Abdelnasser
  • Ait Saidi, Ahmed
  • Bouhmila, Fatah
  • Aissani, Mouloud

Abstract

This paper establishes exponential inequalities for the probability of deviation between the approximate and the exact solution of an operator equation with an exact second member. These inequalities yield the almost complete convergence and the convergence rate of approximate solutions.

Suggested Citation

  • Dahmani, Abdelnasser & Ait Saidi, Ahmed & Bouhmila, Fatah & Aissani, Mouloud, 2009. "Consistency of the Tikhonov's regularization in an ill-posed problem with random data," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 722-727, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:6:p:722-727
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    References listed on IDEAS

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    1. Cardot, Hervé, 2002. "Spatially Adaptive Splines for Statistical Linear Inverse Problems," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 100-119, April.
    2. Bissantz, Nicolai & Hohage, T. & Munk, Axel & Ruymgaart, F., 2007. "Convergence rates of general regularization methods for statistical inverse problems and applications," Technical Reports 2007,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Yurinskii, V. V., 1976. "Exponential inequalities for sums of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 473-499, December.
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