-
1
-
-
0001717185
-
On the convergence of Halley's Method
-
G. Alefeld, On the convergence of Halley's Method, Am. Math. Monthly 88 (1981) 530-536.
-
(1981)
Am. Math. Monthly
, vol.88
, pp. 530-536
-
-
Alefeld, G.1
-
3
-
-
0002836895
-
Halley's method for solving equations
-
H. Bateman, Halley's method for solving equations, Am. Math. Monthly 45 (1938) 11-17.
-
(1938)
Am. Math. Monthly
, vol.45
, pp. 11-17
-
-
Bateman, H.1
-
4
-
-
0040802647
-
On types of convergence and on the behavior of approximations in the neighborhood of a multiple root of an equation
-
E. Bodewig, On types of convergence and on the behavior of approximations in the neighborhood of a multiple root of an equation, Quart. App. Math. 7 (1949) 325-333.
-
(1949)
Quart. App. Math.
, vol.7
, pp. 325-333
-
-
Bodewig, E.1
-
5
-
-
0013201091
-
On Halley's variation of Newton's method
-
G.H. Brown, On Halley's variation of Newton's method, Am. Math. Monthly 84 (1977) 726-728.
-
(1977)
Am. Math. Monthly
, vol.84
, pp. 726-728
-
-
Brown, G.H.1
-
6
-
-
33847195487
-
On the global convergence of Halley's iteration formula
-
M. Davies and B. Dawson, On the global convergence of Halley's iteration formula, Numer. Math. 24 (1975) 133-135.
-
(1975)
Numer. Math.
, vol.24
, pp. 133-135
-
-
Davies, M.1
Dawson, B.2
-
7
-
-
0040406568
-
A variation of Newton's method
-
J.S. Frame, A variation of Newton's method, Am. Math. Monthly 51 (1944) 36-38.
-
(1944)
Am. Math. Monthly
, vol.51
, pp. 36-38
-
-
Frame, J.S.1
-
8
-
-
0043009610
-
Remarks on a variation of Newton's method
-
J.S. Frame, Remarks on a variation of Newton's method, Am. Math. Monthly 52 (1945) 212-214.
-
(1945)
Am. Math. Monthly
, vol.52
, pp. 212-214
-
-
Frame, J.S.1
-
9
-
-
0039814053
-
The solution of equations by continued fraction
-
J.S. Frame, The solution of equations by continued fraction, Am. Math. Monthly 60 (1953) 293-305.
-
(1953)
Am. Math. Monthly
, vol.60
, pp. 293-305
-
-
Frame, J.S.1
-
10
-
-
0000132229
-
On Halley's iteration method
-
W. Gander, On Halley's iteration method, Am. Math. Monthly 92 (1985) 131-134.
-
(1985)
Am. Math. Monthly
, vol.92
, pp. 131-134
-
-
Gander, W.1
-
11
-
-
0028445851
-
Accelerated convergence in Newton's method
-
J. Gerlach, Accelerated convergence in Newton's method, SIAM Rev. 36 (1994) 272-276.
-
(1994)
SIAM Rev.
, vol.36
, pp. 272-276
-
-
Gerlach, J.1
-
12
-
-
0001050260
-
A new, exact, and easy method of finding roots of any equations generally, and that without any previous reduction (Latin)
-
E. Halley, A new, exact, and easy method of finding roots of any equations generally, and that without any previous reduction (Latin), Philos. Trans. Roy. Soc. London 18 (1694) 136-148. [English translation: Philos. Trans. Roy. Soc. London (abridged) 3 (1809) 640-649 (1809).]
-
(1694)
Philos. Trans. Roy. Soc. London
, vol.18
, pp. 136-148
-
-
Halley, E.1
-
13
-
-
0042007915
-
-
abridged 1809
-
E. Halley, A new, exact, and easy method of finding roots of any equations generally, and that without any previous reduction (Latin), Philos. Trans. Roy. Soc. London 18 (1694) 136-148. [English translation: Philos. Trans. Roy. Soc. London (abridged) 3 (1809) 640-649 (1809).]
-
(1809)
Philos. Trans. Roy. Soc. London
, vol.3
, pp. 640-649
-
-
-
14
-
-
0041348853
-
A type of variation of Newton's method
-
H.J. Hamilton, A type of variation of Newton's method, Am. Math. Monthly 57 (1950) 517-522.
-
(1950)
Am. Math. Monthly
, vol.57
, pp. 517-522
-
-
Hamilton, H.J.1
-
15
-
-
0003275962
-
A family of root finding methods
-
E. Hansen and M. Patrick, A family of root finding methods, Numer. Math. 27 (1977) 257-269.
-
(1977)
Numer. Math.
, vol.27
, pp. 257-269
-
-
Hansen, E.1
Patrick, M.2
-
16
-
-
85033109196
-
High order iterative methods for approximating square and cube roots
-
Department of Computer Science, Rutgers University, New Brunswick, NJ
-
B. Kalantari and I. Kalantari, High order iterative methods for approximating square and cube roots, Tech. Report LCSR-TR-213, Department of Computer Science, Rutgers University, New Brunswick, NJ, 1993.
-
(1993)
Tech. Report LCSR-TR-213
-
-
Kalantari, B.1
Kalantari, I.2
-
17
-
-
85033105437
-
High order iterative methods for approximating roots of polynomials
-
Department of Computer Science, Rutgers University, New Brunswick, NJ
-
B. Kalantari and I. Kalantari, High order iterative methods for approximating roots of polynomials, Tech. Report LCSR-TR-214, Department of Computer Science, Rutgers University, New Brunswick, NJ, 1993.
-
(1993)
Tech. Report LCSR-TR-214
-
-
Kalantari, B.1
Kalantari, I.2
-
18
-
-
0001295137
-
High order iterative methods for approximating square roots
-
B. Kalantari and I. Kalantari, High order iterative methods for approximating square roots, BIT 36 (1996) 395-399.
-
(1996)
BIT
, vol.36
, pp. 395-399
-
-
Kalantari, B.1
Kalantari, I.2
-
19
-
-
0019144229
-
A family of one-point iteration formulae for finding roots
-
D.B. Popovski, A family of one-point iteration formulae for finding roots, Internat. J. Comput. Math. 8 (1980) 85-88.
-
(1980)
Internat. J. Comput. Math.
, vol.8
, pp. 85-88
-
-
Popovski, D.B.1
-
20
-
-
14944351893
-
On the geometry of Halley's method
-
T.R. Scavo and J.B. Thoo, On the geometry of Halley's method, Am. Math. Monthly 102 (1995) 417-426.
-
(1995)
Am. Math. Monthly
, vol.102
, pp. 417-426
-
-
Scavo, T.R.1
Thoo, J.B.2
-
21
-
-
0000960921
-
On the geometry of polynomials and a theory of cost: Part I
-
M. Shub and S. Smale, On the geometry of polynomials and a theory of cost: Part I, Ann. Scient. Ec. Norm. Sup. 18 (1985) 107-142.
-
(1985)
Ann. Scient. Ec. Norm. Sup.
, vol.18
, pp. 107-142
-
-
Shub, M.1
Smale, S.2
-
22
-
-
85033125133
-
-
Private communications with the first author
-
S. Smale, Private communications with the first author (1994).
-
(1994)
-
-
Smale, S.1
-
23
-
-
0039222151
-
One more correction formula
-
R.W. Snyder, One more correction formula, Am. Math. Monthly 62 (1955) 722-725.
-
(1955)
Am. Math. Monthly
, vol.62
, pp. 722-725
-
-
Snyder, R.W.1
-
24
-
-
0041000686
-
Another variation of Newton's method
-
J.K. Stewart, Another variation of Newton's method, Am. Math. Monthly 58 (1951) 331-334.
-
(1951)
Am. Math. Monthly
, vol.58
, pp. 331-334
-
-
Stewart, J.K.1
-
26
-
-
0003956960
-
-
F. Ungar Publishing Co., New York
-
B.L. van der Waerden, Algebra, Vol. 1 (F. Ungar Publishing Co., New York, 1970).
-
(1970)
Algebra
, vol.1
-
-
Van Der Waerden, B.L.1
-
27
-
-
0041849576
-
A modification of Newton's method
-
H.S. Wall, A modification of Newton's method, Am. Math. Monthly 55 (1984) 90-94.
-
(1984)
Am. Math. Monthly
, vol.55
, pp. 90-94
-
-
Wall, H.S.1
-
28
-
-
38249013481
-
On two sequences of algorithms for approximating square roots
-
A.K. Yeyios, On two sequences of algorithms for approximating square roots, J. Comput. Appl. Math. 40 (1992) 63-72.
-
(1992)
J. Comput. Appl. Math.
, vol.40
, pp. 63-72
-
-
Yeyios, A.K.1
|