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  • Articles  (5)
  • stability
  • Springer  (5)
  • 1975-1979  (5)
  • Mathematics  (5)
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • Articles  (5)
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  • Springer  (5)
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  • Mathematics  (5)
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
  • Physics  (4)
  • Biology  (2)
  • 1
    Electronic Resource
    Electronic Resource
    A secant method for multiple roots (1977)
    Springer
    BIT 17 (1977), S. 321-328 
    Details
    ISSN: 1572-9125
    Keywords: 5.15 ; nonlinear equation ; root finding ; multiple root ; secant method ; Steffensen procedure ; order of convergence ; efficiency ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A superlinear procedure for finding a multiple root is presented. In it the secant method is applied to the given function divided by a divided difference whose increment shrinks toward zero as the root is approached. Two function evaluations per step are required, but no derivatives need be calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932152
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  • 2
    Electronic Resource
    Electronic Resource
    Stability, prediction-correction, and dynamic programming (1975)
    Springer
    Journal of optimization theory and applications 17 (1975), S. 239-250 
    Details
    ISSN: 1573-2878
    Keywords: Dynamic programming ; approximation methods ; Bolza problem ; stability ; prediction-correction ; reduction of dimensionality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is proven here that a bounded perturbation of the discrete dynamic programming functional equation arising from the Bolza problem yields a bounded change in its solution. This stability property encourages the development of approximation techniques for solving such equations. One such technique, involving the backward solution of an approximate functional equation as a prediction step, followed by a forward reconstruction using true equations as a correction step, is then discussed. Bounds for the errors arising from such an approximation procedure are derived. Successive approximations is suggested, in conclusion, as a means for obtaining improved solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933878
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  • 3
    Electronic Resource
    Electronic Resource
    On a class of linear differential games (1975)
    Springer
    Journal of optimization theory and applications 17 (1975), S. 511-522 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion ; stability ; uncertain systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Saddlepoint strategies are deduced for a class of linear, single-input differential games. Conditions necessary for a saddle-point, as well as sufficient conditions, are discussed. The results are illustrated with a simple example. For the case of one control subject to a norm bound and the other to a quadratic penalty, the results are extended to the vector case and applied to the stabilization of a system subject to norm-bounded input disturbance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932787
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  • 4
    Electronic Resource
    Electronic Resource
    Stabilization through taxation inn-person games (1977)
    Springer
    Journal of optimization theory and applications 23 (1977), S. 277-284 
    Details
    ISSN: 1573-2878
    Keywords: n-person games ; stability ; grand coalition ; taxation systems ; nondominated imputation ; multicriteria framework
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In formulating solutions forn-person cooperative games, the concept of stability has played a dominant role. Although the core concept has the strongest stability, the core of a game is often empty. In this paper, the taxation system is incorporated into our framework, so that a modified solution concept, which enjoys the stability of core, can be developed. Various formulations based on principles such astaxation proportional to income andequity after tax are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933052
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  • 5
    Electronic Resource
    Electronic Resource
    Complete stability of noncooperative games (1978)
    Springer
    Journal of optimization theory and applications 25 (1978), S. 485-505 
    Details
    ISSN: 1573-2878
    Keywords: Game theory ; stability ; contraction mappings
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with a class of noncooperative games ofn players that are defined byn reward functions which depend continuously on the action variables of the players. This framework provides a realistic model of many interactive situations, including many common models in economics, sociology, engineering, and political science. The concept of Nash equilibrium is a suitable companion to such models. A variety of different sufficient conditions for existence, uniqueness, and stability of a Nash equilibrium point have been previously proposed. By sharpening the noncooperative aspect of the framework (which is really only implicit in the original framework), this paper attempts to isolate one set of “natural” conditions that are sufficient for existence, uniqueness, and stability. It is argued thatl ∞ quasicontraction is such a natural condition. The concept of complete stability is introduced to reflect the full character of noncooperation. It is then shown that, in the linear case, the condition ofl ∞ quasicontraction is both necessary and sufficient for complete stability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933516
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