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Computation of Near-Solutions of Operator Equations

In: Generalized Solutions of Operator Equations and Extreme Elements

Author

Listed:
  • D. A. Klyushin

    (Kyiv National Taras Shevchenko University)

  • S. I. Lyashko

    (Kyiv National Taras Shevchenko University)

  • D. A. Nomirovskii

    (Kyiv National Taras Shevchenko University)

  • Yu. I. Petunin

    (Kyiv National Taras Shevchenko University)

  • V. V. Semenov

    (Kyiv National Taras Shevchenko University)

Abstract

Chapter 5 is devoted to numerical aspects of developed theory of generalized solvability. In Sect. 5.2–5.6 we discuss conceptual aspects of reliability and effectiveness of precise and iterative method for solving system of linear algebraic equations obtained as a result of finite-dimensional approximation of initial operator equations. In Sect. 5.7 we prove the criteria of classic solvability of linear operator equations in Banach and Hilbert spaces associated with the Neumann series.

Suggested Citation

  • D. A. Klyushin & S. I. Lyashko & D. A. Nomirovskii & Yu. I. Petunin & V. V. Semenov, 2012. "Computation of Near-Solutions of Operator Equations," Springer Optimization and Its Applications, in: Generalized Solutions of Operator Equations and Extreme Elements, edition 1, chapter 0, pages 103-124, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0619-8_5
    DOI: 10.1007/978-1-4614-0619-8_5
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