Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems

Lucas Jódar; Enrique A. Navarro

Applications of Mathematics (1994)

  • Volume: 39, Issue: 3, page 189-202
  • ISSN: 0862-7940

Abstract

top
In this paper we obtain existence conditions and a closed form of the general solution of higher order singular regular boundary value problems. The approach is based on the concept of co-solution of algebraic matrix equations of polynomial type that permits the treatment of the problem without considering an extended first order system as it has been done in the known literature.

How to cite

top

Jódar, Lucas, and Navarro, Enrique A.. "Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems." Applications of Mathematics 39.3 (1994): 189-202. <http://eudml.org/doc/32878>.

@article{Jódar1994,
abstract = {In this paper we obtain existence conditions and a closed form of the general solution of higher order singular regular boundary value problems. The approach is based on the concept of co-solution of algebraic matrix equations of polynomial type that permits the treatment of the problem without considering an extended first order system as it has been done in the known literature.},
author = {Jódar, Lucas, Navarro, Enrique A.},
journal = {Applications of Mathematics},
keywords = {algebraic matrix equation; co-solution; singular regular system; boundary value problem; Drazin inverse; closed form solution; closed form expression; multi-point boundary values; co-solution of algebraic matrix equations},
language = {eng},
number = {3},
pages = {189-202},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems},
url = {http://eudml.org/doc/32878},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Jódar, Lucas
AU - Navarro, Enrique A.
TI - Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 3
SP - 189
EP - 202
AB - In this paper we obtain existence conditions and a closed form of the general solution of higher order singular regular boundary value problems. The approach is based on the concept of co-solution of algebraic matrix equations of polynomial type that permits the treatment of the problem without considering an extended first order system as it has been done in the known literature.
LA - eng
KW - algebraic matrix equation; co-solution; singular regular system; boundary value problem; Drazin inverse; closed form solution; closed form expression; multi-point boundary values; co-solution of algebraic matrix equations
UR - http://eudml.org/doc/32878
ER -

References

top
  1. 10.1016/0024-3795(87)90219-9, Linear Algebra Appl. 85 (1987), 221–239. (1987) MR0869356DOI10.1016/0024-3795(87)90219-9
  2. Singular Systems of Differential Equations, Pitman Pubs. Co., 1980. (1980) Zbl0419.34007
  3. Generalized Inverses of Linear Transformations, Pitman Pubs. Co., 1979. (1979) 
  4. Modern Control Systems, Addison-Wesley Pubs. Co., 1974. (1974) 
  5. A minimax theory of overdamped networks, J. Rat. Mech. and Anal. 4 (1955), 221–223. (1955) MR0069030
  6. 10.1016/0022-247X(64)90072-1, J. Math. Anal. and Appl. 8 (1963), 325–331. (1963) MR0162005DOI10.1016/0022-247X(64)90072-1
  7. 10.1512/iumj.1981.30.30027, Ind. J. Math. 30 (1981), 321–356. (1981) MR0611224DOI10.1512/iumj.1981.30.30027
  8. 10.1216/RMJ-1982-12-4-591, Rocky Mountain J. Maths. 12 (1982), 591–614. (1982) MR0683854DOI10.1216/RMJ-1982-12-4-591
  9. Rectangular co-solutions of polynomial matrix equations and applications, Applied Maths. Letters 4(2) (1991), 13–16. (1991) MR1095642
  10. The Laurent expansion of a nearly singular matrix, Linear Algebra Appls. 4 (1971), 329–340. (1971) MR0371934
  11. MACSYMA, MACSYMA Symbolic Inc., 1989. (1989) Zbl0745.33007
  12. MATLAB User’s guide, Tech. Rep. CS81, Department of Computer Science, Univ. of Mexico, Alburquerque, New Mexico 87131, 1980. (1980) 
  13. Numerical Analysis, A second course, Academic Press, 1972. (1972) Zbl0248.65001MR0403154
  14. The Method of Discretization in Time and Partial Differential Equations, D. Reidel Pubs. Co., 1982. (1982) Zbl0522.65059MR0689712
  15. Generalized Inverse of Matrices and its Applications, John Wiley, 1971. (1971) MR0338013

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.