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2001 | 11 | 5 | 1025-1033

Tytuł artykułu

Numerical analysis and systems theory

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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.

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  • Deptartment of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, U.S.A.


  • Alexandrov N.M. and Hussaini M.Y. (Eds) (1997): Multi Disciplinary Design Optimization: State of the Art. — Philadelphia: SIAM.
  • Antoulas A.C. and Sorensen D.C. (2001): Approximation in large-scale dynamical systems: An overview. — this issue.
  • Benner P., Quintana-Orti E.S. and Quintana-Orti G. (2001): Efficient numerical algorithms for balanced stochastic truncation. — this issue.
  • Betts J.T. (2001): Practical Methods for Optimal Control Using Nonlinear Programming. — Philadelphia: SIAM.
  • 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).
  • Betts J., Biehn N. and Campbell S.L. (2001): Convergence of nonconvergent IRK discretizations of optimal control problems with state inequality constraints. — preprint.
  • Borggaard J.T., Burns J., Cliff E. and Schreck S. (1998): Computational Methods in Optimal Design and Control. — Boston: Birkhäuser.
  • Brenan K.E., Petzold L.R. and Campbell S.L. (1996): Numerical Solution of Initial Value Problems in Differential Algebraic Equations. — Philadelphia: SIAM.
  • Bunch J.R., Le Borne R.C. and Proudler I.K. (2001): Measuring and maintaining consistency: A hybrid FTF algorithm. — this issue.
  • Calvetti D., Lewis B. and Reichel L. (2001): On the choice of subspace for iterative methods for linear discrete ill-posed systems. — this issue.
  • 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.
  • Chu E.K. (2001): Optimization and pole assignment in control system design. — this issue.
  • Datta B.N. (1999): Applied and Computational Control, Signals, and Circuits. — Boston: Birkhäuser.
  • Enqvist P. (2001): A homotopy approach to rational covariance extension with degree constraint. — this issue.
  • Golub G.H. and Dooren P.V. (Eds.) (1991): Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms. — Berlin: Springer-Verlag.
  • Gomez C. (Ed.) (1999): Engineering and Scientific Computing with SciLab. — Boston: Birkhauser.
  • Gustafsson K. (1993): Object-oriented implementation of software for solving ordinary differential equations. — Sci. Prog., Vol.2, No.4, pp.217–225.
  • 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.
  • 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.
  • 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.
  • Hall G. and Usman A. (2001): Modified order and stepsize strategies in Adams codes. — J. Comp. Appl. Math., to appear.
  • Li J. and White J. (2001): Reduction of large circuit models via low rank approximate Gramians. — this issue.
  • Mokhtari M. and Marie M. (2000): Engineering applications of MATLAB 5.3 and Simulink 3. — Springer-Verlag.
  • van Overschee P. and de Moor B. (1996): Subspace Identification for Linear System Theory, Implementation, Applications. — Boston: Kluwer.
  • Pichler F., Moreno-Diaz R. and Albrecht R. (Eds.) (2000): Computer Aided Systems Theory—EUROCAST 99. — Berlin: Springer-Verlag.
  • Pytlak R. (1999): Numerical Methods for Optimal Control Problems with State Constraints. — Berlin: Springer.
  • Söderlind G. (1998): The automatic control of numerical integration. — CWI Quart., Vol.11, No.1, pp.55–74.
  • Usman A. and Hall G. (1998): Equilibrium states for predicter-corrector methods. — J. Comp. Appl. Math., Vol.89, No.2, pp.275–308.
  • Varga A. (2001): Computing generalized inverse systems using matrix pencil methods. — this issue.

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