[Back to Results | New Search]

Student Number 87221013 Author T-Xin Wang(¤ý²Î·s) Author's Email Address No Public. Statistics This thesis had been viewed 1476 times. Download 542 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

Reference.....................................................................................40Reference [1] J. K. Baksalary and R. Kala, The matrix equation AX-YB=C, Linear Algebra Appl., 25:41-43, 1979.

[2] J. K. Baksalary and R. Kala, The matrix equation

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.

[4] S. Campbell, Numerical solution of higher index linear time varying singular systems of DAEs., SIAM J. Scient. Stat. Comp. 6, 334-348, 1988.

[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..

[7] K.-W. E. Chu, Singular value and generalized singular value decompositions and the solution of linear matrix equations, Linear Algebra and its Appl., 88/89:83-98, 1987.

[8] L. Dieci and T. Eirola, On smooth decompositions of matrices, SIAM J. Matrix Anal. Appl., 20:800-819, 1999.

[9] F. R. Gantmacher, The theory of Matrices Vol II, Chelsea, New York, 1959.

[10] G. H. Golub and C. F. Van Loan, Matrix Computations, The Johns Hopkins University Press, 2nd edition, 1989.

[11] J. K. Hale, Ordinary Differential Equations, Krieger Publishing Co, Malabar, 1980.

[12] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.

[13] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.

[14] P. Kunkel and V. Mehrmann, Canonical forms for linear DAEs with variable coefficients, J. Comp. Appl. Math. 56:225-251, 1994.

[15] E. V. Mamontov, Some properties of a system of first order ordinary differential nonlinear equations with a singular

matrix of constant rank in front of the vector of the derivatives, Differentsialnye Uravneniya, 24:1055-1058, 1988.

[16] M. Z. Nashed (Ed), Generalized Inverses and Applications, New York: Academic, 1976.

[17] C. C. Paige and M. A. Saunders, Towards a generalized singular value decomposition, SIAM J. Numer Anal., 18:398-405, 1981.

[18] Y. Sibuya, Some global properties of matrices of functions of one variable, Math. Annal., 161:67-77, 1965.

[19] G. W. Stewart, Introduction to Matrix Computations, New York: Academic Press, 1973.

[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(³¯«Ø¶©)

Files approve immediately

87221013.pdf Date of Submission 2000-07-19

Our service phone is (03)422-7151 Ext. 57407,E-mail is also welcomed.