• 제목/요약/키워드: quadratic equation

검색결과 537건 처리시간 0.025초

Minimization Method for Solving a Quadratic Matrix Equation

  • Kim, Hyun-Min
    • Kyungpook Mathematical Journal
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    • 제47권2호
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    • pp.239-251
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    • 2007
  • We show how the minimization can be used to solve the quadratic matrix equation and then compare two different types of conjugate gradient method which are Polak and Ribi$\acute{e}$re version and Fletcher and Reeves version. Finally, some results of the global and local convergence are shown.

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SOLUTION AND STABILITY OF A GENERAL QUADRATIC FUNCTIONAL EQUATION IN TWO VARIABLES

  • LEE, EUN HWI;LEE, JO SEUNG
    • 호남수학학술지
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    • 제26권1호
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    • pp.45-59
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    • 2004
  • In this paper we obtain the general solution the functional equation $a^2f(\frac{x-2y}{a})+f(x)+2f(y)=2a^2f(\frac{x-y}{a})+f(2y).$ The type of the solution of this equation is Q(x)+A(x)+C, where Q(x), A(x) and C are quadratic, additive and constant, respectively. Also we prove the stability of this equation in the spirit of Hyers, Ulam, Rassias and $G\check{a}vruta$.

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RICCATI EQUATION IN QUADRATIC OPTIMAL CONTROL PROBLEM OF DAMPED SECOND ORDER SYSTEM

  • Ha, Junhong;Nakagiri, Shin-Ichi
    • 대한수학회지
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    • 제50권1호
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    • pp.173-187
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    • 2013
  • This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a general class of the second order distributed systems with arbitrary damping terms.

HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

  • Trif, Tiberiu
    • 대한수학회보
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    • 제40권2호
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    • pp.253-267
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    • 2003
  • In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.

FOR THE HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

  • Lee, Eun-Hwi;Chang, Ick-Soon
    • Journal of applied mathematics & informatics
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    • 제15권1_2호
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    • pp.435-446
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    • 2004
  • In this paper, we obtain the general solution of a quadratic functional equation $b^2f(\frac{x+y+z}{b})+f(x-y)+f(x-z)=\;a^2[f(\frac{x-y-z}{a})+f(\frac{x+y}{a})+f(\frac{x+z}{a})]$ and prove the stability of this equation.

On the Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation

  • Lee, Young-Whan;Park, Sun-Hui
    • Journal of applied mathematics & informatics
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    • 제9권1호
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    • pp.371-380
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    • 2002
  • In this paper we obtain the general solution of a quadratic Jensen type functional equation : (equation omitted) and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

A FUNCTIONAL EQUATION RELATED TO QUADRATIC FORMS WITHOUT THE CROSS PRODUCT TERMS

  • Park, Won-Gil;Bae, Jae-Hyeong
    • 호남수학학술지
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    • 제30권2호
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    • pp.219-225
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    • 2008
  • In this paper, we obtain the general solution and the stability of the 2-dimensional vector variable quadratic functional equation f( x + y, z - w) + f(x - y, z + w) = 2f(x, z ) + 2f(y, ${\omega}$). The quadratic form f( x, y) = $ax^2$ + $by^2$ without cross product terms is a solution of the above functional equation.