Variable Coefficients Linear Higher-Order Differential-Algebraic Equations

[5] E. A. Coddington, R. Carlson. Linear Ordinary Di_erential Equations. SIAM. Philadelphia. 1997. [6] R. Courant, F. John. Introduction to Calculus and Analysis I. Springer-Verlag, New York, Inc. 1989. [7] S. L. Campbell. Singular Systems of Di_erential Equations. Pitman, Boston, 1980. [8] S. L. Campbell. Singular Systems of Di_erential Equations II. Pitman, Boston, 1982. [9] E. K.-W. Chu. Perturbation of eigenvalues for matrix polynomials via the Bauer{ Fike theorems. SIAM J. Matrix Anal. Appl. 25(2003), pp. 551-573. [10] E. A. Coddington, N. Levinson. Theory of Ordinary Di_erential Equations. McGraw-Hill Book Company, Inc. 1955. [11] C. De Boor, H. O. Kreiss. On the condition of the linear systems associated with discretized BVPs of ODEs. SIAM J. Numer. Anal., Vol 23, 1986, pp. 936-939. [12] J. Demmel. Applied Numerical Linear Algebra. SIAM Press. 1997. [13] J. -P. Dedieu, F, Tisseur. Perturbation theory for homogeneous polynomial eigenvalue problems. Lin. Alg. Appl., 358: 71-74, 2003. [14] F. R. Gantmacher. The Theory of Matrices. Vol. I. Chelsea Publishing Company, New York, 1959. [15] F. R. Gantmacher. The Theory of Matrices. Vol. II. Chelsea Publishing Company, New York, 1959. [16] E. Griepentrog, M. Hanke and R. M•arz. Toward a better understanding of differential algebraic equations (Introductory survey). Seminar Notes Edited by E. Griepentrog, M. Hanke and R. M•arz, Berliner Seminar on Di_erential-Algebraic Equations, 1992. http://www.mathematik.hu-berlin.de/publ/SB-92-1/s Differential-Algebraic Equations.html [17] I. Gohberg, P. Lancaster, L. Rodman. Matrix Polynomials. Academic Press. 1982. [18] E. Griepentrog, R. M•arz. Di_erential-Algebraic Equations and Their Numerical Treatment. Teubner-Texte zur Mathematik, Band 88, 1896.

University Press. 1996. [20] N. J. Higham. Matrix nearness problems and applications. In M. J. C. Gover and S. Barnett, editors, Applications of Matrix Theory, pages 1-27, Oxford University Press, 1989. [21] D. J. Higham, N. J. Higham. Structured backward error and condition of generalized eigenvalue problems. SIAM J. Matrix Anal. Appl. 20 (2) (1998) 493-512. [22] N. J. Higham, F. Tisseur. More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Lin. Alg. Appl., 351-352: 435-453, 2002. [23] N. J. Higham, F. Tisseur. Bounds for Eigenvalues of Matrix Polynomials. Lin. Alg. Appl., 358: 5-22, 2003. [24] N. J. Higham, F. Tisseur, and P. M. Van Dooren. Detecting a de_nite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems. Lin. Alg. Appl., 351-352: 455-474, 2002. [25] R. A. Horn, C. R. Johnson. Matrix Analysis. Cambridge University Press, July, 1990. [26] T.-M. Hwang, W.-W. Lin and V. Mehrmann. Numerical solution of quadratic eigenvalue problems with structure-preserving methods. SIAM J. Sci. Comput. 24:1283-1302, 2003. [27] P. Kunkel and V. Mehrmann. Smooth factorizations of matrix valued functions and their derivatives. Numer. Math. 60: 115-132, 1991. [28] P. Kunkel and V. Mehrmann. Canonical forms for linear di_erential-algebraic equations with variable coe_cients. J. Comp. Appl. Math. 56(1994), 225-251. [29] P. Kunkel and V. Mehrmann. A new look at pencils of matrix valued functions. Lin. Alg. Appl., 212/213: 215-248, 1994. [30] P. Kunkel and V. Mehrmann. Local and global invariants of linear di_erentialalgebraic equations and their relation. Electron. Trans. Numer. Anal. 4: 138-157, 1996. [31] P. Kunkel and V. Mehrmann. A new class of discretization methods for the solution of linear di_erential-algebraic equations. SIAM J. Numer. Anal. 33: 1941-1961, 1996.