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Student Number 87221013
Author T-Xin Wang(ηs)
Author's Email Address No Public.
Statistics This thesis had been viewed 1450 times. Download 528 times.
Department Mathematics
Year 1999
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title Smooth and Periodic Minimal l_2-Solutions of Some Linear Matrix Equations
Date of Defense 2000-07-19
Page Count 41
Keyword
  • minimal l_2 solution
  • smooth and periodic
  • Abstract Periodic matrices arise quite often in the study of dynamics.
    The matrices with constant rank is important in applications related to differential algebraic system.In this paper we consider the following smooth and periodic linear matrix equations with constant rank matrix coefficients respectively.
    (1.1) A(t)x(t)=b(t),
    (1.2) A(t)X(t)B(t)=E(t),
    (1.3) A(t)X(t) + Y(t)B(t)=C(t),
    (1.4) A(t)X(t)B(t) + C(t)Y(t)D(t)=E(t).
    Because they may be inconsistent (i.e., have no solution),
    we are interesting in the following smooth and periodic minimal l_2-solution problems respectively.
    (1.1a) min||A(t)x(t)-b(t)||_2
    (1.2a) min||A(t)X(t)B(t)-E(t)||_2
    (1.3a) min||A(t)X(t)+Y(t)B(t)-C(t)||_2
    (1.4a) min||A(t)X(t)B(t)+C(t)Y(t)D(t)-E(t)||_2
    Table of Content 1 Introduction................................................................................1
    2 Preliminaries...............................................................................4
    3 Smooth and periodic minimal `2-solution of problem (1.1a)........7
    4 Smooth and periodic minimal `2-solution of problem (1.2a)......11
    5 Smooth and periodic minimal `2-solution of problem (1.3a)......18
    6 Smooth and periodic minimal `2-solution of problem (1.4a)......25
    Reference.....................................................................................40
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    AXB+CYD=E, Linear Algebra Appl., 30:141-147, 1980.
    [3] K. E. Brebnan, S. L. Campbell and L. R. Petzold, Numerical solution of IVPs in DAEs., North-Holland, New York, 1989.
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    [5] J.-L. Chern, The smooth SSVD of periodic complex symmetric metrices, Preprint.
    [6] J.-L. Chern and L. Dieci, Smoothness and periodicity of some matrix decompositions, to appear in SIAM J. Matrix Anal. Appl..
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    [15] E. V. Mamontov, Some properties of a system of first order ordinary differential nonlinear equations with a singular
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    [20] K. Zietak, On a particular case of the inconsistent linear matrix equation AX+YB=C, Linear Algebra and its Appl., 66:249-258, 1985.
    Advisor
  • Jann-Long Chern(ض)
  • Files
  • 87221013.pdf
  • approve immediately
    Date of Submission 2000-07-19

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