| Title:
|
Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems (English) |
| Author:
|
Jódar, Lucas |
| Author:
|
Navarro, Enrique |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
189-202 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
algebraic matrix equation |
| Keyword:
|
co-solution |
| Keyword:
|
singular regular system |
| Keyword:
|
boundary value problem |
| Keyword:
|
Drazin inverse |
| Keyword:
|
closed form solution |
| MSC:
|
34A08 |
| MSC:
|
34B10 |
| idZBL:
|
Zbl 0814.34014 |
| idMR:
|
MR1273632 |
| DOI:
|
10.21136/AM.1994.134252 |
| . |
| Date available:
|
2009-09-22T17:43:44Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134252 |
| . |
| Reference:
|
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| Reference:
|
[2] S. L. Campbell: Singular Systems of Differential Equations.Pitman Pubs. Co., 1980. Zbl 0419.34007 |
| Reference:
|
[3] S. L. Campbell and C. D. Meyer, jr.: Generalized Inverses of Linear Transformations.Pitman Pubs. Co., 1979. |
| Reference:
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[4] R. C. Dorf: Modern Control Systems.Addison-Wesley Pubs. Co., 1974. |
| Reference:
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| Reference:
|
[6] R. J. Duffin: Chrystal’s theorem on differential equations systems.J. Math. Anal. and Appl. 8 (1963), 325–331. MR 0162005, 10.1016/0022-247X(64)90072-1 |
| Reference:
|
[7] I. Gohberg, M. A. Kaashoek, L. Lerer and L. Rodman: Common multiples and common divisors of matrix polynomials, I. Spectral method.Ind. J. Math. 30 (1981), 321–356. MR 0611224, 10.1512/iumj.1981.30.30027 |
| Reference:
|
[8] J. W. Hooker and C. E. Langenhop: On regular systems of linear differential equations with constant coefficients.Rocky Mountain J. Maths. 12 (1982), 591–614. MR 0683854, 10.1216/RMJ-1982-12-4-591 |
| Reference:
|
[9] L. Jódar and E. Navarro: Rectangular co-solutions of polynomial matrix equations and applications.Applied Maths. Letters 4(2) (1991), 13–16. MR 1095642 |
| Reference:
|
[10] C. E. Langenhop: The Laurent expansion of a nearly singular matrix.Linear Algebra Appls. 4 (1971), 329–340. MR 0371934 |
| Reference:
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[11] : MACSYMA.MACSYMA Symbolic Inc., 1989. Zbl 0745.33007 |
| Reference:
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[12] C. B. Moler: MATLAB User’s guide, Tech. Rep. CS81.Department of Computer Science, Univ. of Mexico, Alburquerque, New Mexico 87131, 1980. |
| Reference:
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[13] J. M. Ortega: Numerical Analysis, A second course.Academic Press, 1972. Zbl 0248.65001, MR 0403154 |
| Reference:
|
[14] K. Rektorys: The Method of Discretization in Time and Partial Differential Equations.D. Reidel Pubs. Co., 1982. Zbl 0522.65059, MR 0689712 |
| Reference:
|
[15] C. R. Rao and S. K. Mitra: Generalized Inverse of Matrices and its Applications.John Wiley, 1971. MR 0338013 |
| . |
