The area of numerical analysis interacts with the area of control and systems theory in a number of ways, some of which are widely recognized and some of which are not fully appreciated or understood. This paper will briefly discuss some of these areas of interaction and place the papers in this volume in context.
@article{bwmeta1.element.bwnjournal-article-amcv11i5p1025bwm, author = {Campbell, Stephen}, title = {Numerical analysis and systems theory}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {11}, year = {2001}, pages = {1025-1033}, zbl = {1002.93004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i5p1025bwm} }
Campbell, Stephen. Numerical analysis and systems theory. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 1025-1033. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i5p1025bwm/
[000] Alexandrov N.M. and Hussaini M.Y. (Eds) (1997): Multi Disciplinary Design Optimization: State of the Art. — Philadelphia: SIAM.
[001] Antoulas A.C. and Sorensen D.C. (2001): Approximation in large-scale dynamical systems: An overview. — this issue.
[002] Benner P., Quintana-Orti E.S. and Quintana-Orti G. (2001): Efficient numerical algorithms for balanced stochastic truncation. — this issue. | Zbl 1008.93014
[003] Betts J.T. (2001): Practical Methods for Optimal Control Using Nonlinear Programming. — Philadelphia: SIAM. | Zbl 0995.49017
[004] Betts J.T., Biehn N., Campbell S.L. and Huffman W.P. (2000): Convergence of nonconvergent IRK discretizations of optimal control problems. — Proc. IMACS 2000, Lausanne (CD- ROM). | Zbl 1009.49025
[005] Betts J., Biehn N. and Campbell S.L. (2001): Convergence of nonconvergent IRK discretizations of optimal control problems with state inequality constraints. — preprint. | Zbl 1009.49025
[006] Borggaard J.T., Burns J., Cliff E. and Schreck S. (1998): Computational Methods in Optimal Design and Control. — Boston: Birkhäuser.
[007] Brenan K.E., Petzold L.R. and Campbell S.L. (1996): Numerical Solution of Initial Value Problems in Differential Algebraic Equations. — Philadelphia: SIAM. | Zbl 0844.65058
[008] Bunch J.R., Le Borne R.C. and Proudler I.K. (2001): Measuring and maintaining consistency: A hybrid FTF algorithm. — this issue. | Zbl 1001.93054
[009] Calvetti D., Lewis B. and Reichel L. (2001): On the choice of subspace for iterative methods for linear discrete ill-posed systems. — this issue. | Zbl 0994.65043
[010] Campbell S., Biehn N., Jay L. and Westbrook T. (2000): Some comments on DAE theory for IRK methods and trajectory optimization. — J. Comp. Appl. Math., Vol.120, No.1–2, pp.109–131. | Zbl 0956.65070
[011] Chu E.K. (2001): Optimization and pole assignment in control system design. — this issue.
[012] Datta B.N. (1999): Applied and Computational Control, Signals, and Circuits. — Boston: Birkhäuser. | Zbl 0934.00020
[013] Enqvist P. (2001): A homotopy approach to rational covariance extension with degree constraint. — this issue.
[014] Golub G.H. and Dooren P.V. (Eds.) (1991): Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms. — Berlin: Springer-Verlag.
[015] Gomez C. (Ed.) (1999): Engineering and Scientific Computing with SciLab. — Boston: Birkhauser. | Zbl 0949.68606
[016] Gustafsson K. (1993): Object-oriented implementation of software for solving ordinary differential equations. — Sci. Prog., Vol.2, No.4, pp.217–225.
[017] Gustafsson K. (1994): Control-theoretic techniques for stepsize selection in implicit Runge- Kutta methods. — ACM Trans. Math. Softw., Vol.20, No.4, pp.496–517. | Zbl 0888.65096
[018] Gustafsson K., Lundh M. and Söderlind G. (1988): A PI stepsize control for the numerical integration of ordinary differential equations. — BIT, Vol.28, No.2, pp.270–287. | Zbl 0645.65039
[019] Gustafsson K. and Söderlind G. (1997): Control Strategies for the Iterative Solution of Nonlinear Equations in ODE Solvers. — SIAM J. Sci. Stat. Comp., Vol.18, No.1, pp.23–40. | Zbl 0867.65035
[020] Hall G. and Usman A. (2001): Modified order and stepsize strategies in Adams codes. — J. Comp. Appl. Math., to appear. | Zbl 0941.65076
[021] Li J. and White J. (2001): Reduction of large circuit models via low rank approximate Gramians. — this issue.
[022] Mokhtari M. and Marie M. (2000): Engineering applications of MATLAB 5.3 and Simulink 3. — Springer-Verlag.
[023] van Overschee P. and de Moor B. (1996): Subspace Identification for Linear System Theory, Implementation, Applications. — Boston: Kluwer. | Zbl 0888.93001
[024] Pichler F., Moreno-Diaz R. and Albrecht R. (Eds.) (2000): Computer Aided Systems Theory—EUROCAST 99. — Berlin: Springer-Verlag.
[025] Pytlak R. (1999): Numerical Methods for Optimal Control Problems with State Constraints. — Berlin: Springer. | Zbl 0928.49002
[026] Söderlind G. (1998): The automatic control of numerical integration. — CWI Quart., Vol.11, No.1, pp.55–74. | Zbl 0922.65063
[027] Usman A. and Hall G. (1998): Equilibrium states for predicter-corrector methods. — J. Comp. Appl. Math., Vol.89, No.2, pp.275–308. | Zbl 0905.65088
[028] Varga A. (2001): Computing generalized inverse systems using matrix pencil methods. — this issue. | Zbl 1031.93071