Solving Linear Boundary Value Problems Via Non-commutative Gröbner Bases

References

• Bachmair , L. and Ganzinger , H. 1994 . “ Buchberger’s algorithm: a constraint-based completion procedure ” . In First International Conference on Constraints in Computational Logics , Edited by: Jouannaud , J.-P. 285 – 301 . München : Springer . Vol. 845 of Lecture Notes in Computer Science
   Google Scholar
• M.A. Borges and Mijail Borges. Gröbner bases property on elimination ideal in the noncommutative case. In [7] 323–337.
   Google Scholar
• B. Buchberger (1965) An algorithm for finding a basis for the residual class ring of zero-dimensional polynomial ideal (German). PhD Thesis, University of Innsbruck, Institute for Mathematics.
   Google Scholar
• Buchberger , B. 1970 . An algorithmic criterion for the solvability of algebraic systems of equations (German) . Æquationes Mathematicae , 4 : 374 – 383 .
   Google Scholar
• B. Buchberger (1999). Theory exploration versus theorem proving, invited conference talk at Calculemus ’99, Trento, Italy. Available as RISC technical report at http:ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-46.tar.gz (http:ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-46.tar.gz)
   Google Scholar
• B. Buchberger. Introduction to Gröbner bases. In: [7], 3–31.
   Google Scholar
• Buchberger , B. and Winkler , Franz , eds. 1998 . Gröbner bases and applications , Cambridge : London Mathematical Society, Lecture Note Series 251, Cambridge University Press .
   Google Scholar
• Coddington , E.A. and Levinson , N. 1995 . Theory of Ordinary Differential Equations , New York : McGraw-Hill Book Company .
   Google Scholar
• Courant , R. and Hilbert , D. 1993 . Die Methoden der mathematischen Physik , 4th edition , Vol. 1 & 2 , Berlin : Springer .
   Google Scholar
• Davenport , J.H. , Siret , Y. and Tournier , E. 1998 . Computer Algebra , London : Academic Press .
   Google Scholar
• Engl , H.W. , Hanke , M. and Neubauer , A. 1996 . Regularization of Inverse Problems , Dordrecht : Kluwer .
   Google Scholar
• Engl , H.W. and Nashed , M.Z. 1981 . New extremal characterizations of generalized inverses of linear operators . Journal of Mathematical Analysis and Applications , 82 : 566 – 586 .
   Web of Science ®Google Scholar
• Grosche , G. , Ziegler , V. and Ziegler , D. 1996 . Teubner-Taschenbuch der Mathematik , Stuttgart : Teubner .
   Google Scholar
• J.W. Helton and Robert L. Miller. The system NCAlgebra, homepage and manual at http://math.ucsd.edu/ñcalg, http://math.ucsd.edu/ñcalg/NCBIGDOC/NCBIGDOC.html.
   Google Scholar
• Helton , J. William , Stankus , Mark and Wavrik , John . 1998 . Computer simplification of engineering systems formulas . IEEE Trans. Autom. Control , 43/3 : 302 – 314 .
   Web of Science ®Google Scholar
• Helton , J. William and Wavrik , John . 1994 . Rules for computer simplification of the formulas in operator model theory and linear systems . Operator Theory: Advances and Applications , 73 : 325 – 354 .
   Google Scholar
• Krall , A.M. 1986 . Applied Analysis , Dordrecht : D. Reidel Publishing Company .
   Google Scholar
• Loud , W. 1970 . Some examples of generalized green’s functions and generalized green’s matrices . SIAM Review , 12 ( 2 ) : 194 – 210 .
   Web of Science ®Google Scholar
• Man , Y.-K. 1983 . Computing closed form solutions of first order ODES using the Prelle-singer procedure . Journ. Symb. Comp. , 16 : 423 – 443 .
   Web of Science ®Google Scholar
• Marché , C. 1996 . Normalized rewriting: an alternative to rewriting modulo a set of equations . Journ. Symb. Comp. , 11 : 1 – 36 .
   Google Scholar
• Nashed , M.Z. , ed. 1976 . “ Generalized inverses and applications ” . In Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center , New York : Academic Press .
   Google Scholar
• M.Z. Nashed. Aspects of generalized inverses in analysis and regularization. In: [21], 193–244.
   Google Scholar
• Prelle , M.J. and Singer , M. F. 1983 . Elementary first integrals of differential equations . Trans. AMS , 279/1 : 215 – 229 .
   Web of Science ®Google Scholar
• D.C. Struppa. Grböner bases in partial differential equations. In: [7], 235–245.
   Google Scholar
• Stakgold , I. 1979 . Green’s Functions and Boundary Value Problems , New York : John Wiley & Sons .
   Google Scholar
• Wavrik , J. 1996 . Rewrite rules and simplification of matrix expressions . Computer Science Journal of Moldova , 4/2/11 (1996).
   Google Scholar