Convergence behaviour of the Newton iteration for first order differential equations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 72 LNCS, Issue , 1979, Pages 189-199

  Geddes, K O ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; DIFFERENTIAL EQUATIONS;

ALGEBRAIC FUNCTIONS; FIRST ORDER DIFFERENTIAL EQUATION; FIRST ORDER NONLINEAR DIFFERENTIAL EQUATIONS; NEWTON ITERATIONS; POWER SERIES; POWER SERIES SOLUTIONS; TYPICAL APPLICATION;

NONLINEAR EQUATIONS;

EID: 85025499255     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-09519-5_71     Document Type: Conference Paper

References (9)

1. W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 3rd ed. John Wiley and Sons, New York, 1977.
2. R.P. Brent, Multiple-precision zero-finding methods and the complexity of elementary function evaluation. In Analytic Computational Complexity, J.F. Traub, Ed., Academic Press, New York, 1976, pp. 151-176.
3. R.P. Brent and H.T. Kung, Fast Algorithms for manipulating formal power series. J.ACM 25, 4 (Oct. 1978), pp. 581-595.
4. H.T. Kung and J.F. Traub, All algebraic functions can be computed fast. J.ACM 25, 2 (Apr. 1978), pp. 245-260.
5. J.D. Lipson, Newton’s method: a great algebraic algorithm. In Proc. 1976 ACM Symp. on Symbolic and Algebraic Comput., R.D. Jenks, Ed., pp. 260-270.
6. A.C. Norman, Computing with formal power series. ACM Trans. Math. Software 1, 4 (Dec. 1975), pp. 346-356.
7. D.Y.Y. Yun, Hensel meets Newton - Algebraic constructions in an analytic setting. In Analytic Computational Complexity, J.F. Traub, Ed., Academic Press, New York, 1976, pp. 205-216.
8. D.Y.Y. Yun, Algebraic algorithms using p-adic constructions. In Proc. 1976 ACM Symp. on Symbolic and Algebraic Comput., R.D. Jenks, Ed., pp. 248-259.
9. R.E. Zippel, Univariate power series expansions in algebraic manipulation. In Proc. 1976 ACM Symp. on Symbolic and Algebraic Comput., R.D. Jenks, Ed., pp. 198-208.