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Student Number 87221013 Author T-Xin Wang(¤ý²Î·s) Author's Email Address No Public. Statistics This thesis had been viewed 1457 times. Download 531 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)||_2Table 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

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