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Secant modification of Newton's method

1958
*
Communications of the ACM
*

*SECANT*

*MODIFICATION*

*OF*

*NEWTON’S*

*METHOD*T. A. ... The

*secant*

*method*also has the advantage

*of*needing less memory space.

*Newton’s*iterative scheme for finding a root

*of*f(x) =0 is £(Xn) ee TD Denoting the error by ¢,=x. ...

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On the Modification of Newton-Secant Method in Solving Nonlinear Equations for Multiple Zeros of Trigonometric Function

2021
*
CAUCHY
*

The obtained results from the analysis

doi:10.18860/ca.v7i1.12934
fatcat:jjj5pezmkzao3mtgnp6arkhqcq
*of**modification**of*Newton-*Secant**method*is an iteration formula*of*the modified Newton-*Secant**method*. ... This study discusses the analysis*of*the*modification**of*Newton-*Secant**method*and solving nonlinear equations having a multiplicity*of*by using a modified Newton-*Secant**method*. ... using the*modification**of*Newton-*Secant**method*formula. 7) Comparing the*modification**of*Newton-*Secant**method*with the*Newton's**method*, the*Secant**method*, and the Newton-*Secant**method*. ...##
###
Page 9 of Communications of the Association for Computing Machinery Vol. 1, Issue 8
[page]

1958
*
Communications of the Association for Computing Machinery
*

*SECANT*

*MODIFICATION*

*OF*

*NEWTON’S*

*METHOD*T. A. ... The

*secant*

*method*also has the advantage

*of*needing less memory space.

*Newton’s*iterative scheme for finding a root

*of*f(x) =0 is £(Xn) ee TD Denoting the error by ¢,=x. ...

##
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Problems and solutions by the application of Julia set theory to one-dot and multi-dots numerical methods

2001
*
International Journal of Mathematics and Mathematical Sciences
*

It is known that the application

doi:10.1155/s0161171201011887
fatcat:fpcd4aqgtjfenkyw2mlzhwn65m
*of*Julia set theory is possible to the one-dot numerical*method*like the*Newton's**method*for computing solution*of*the nonlinear equations. ... Previously we have defined two one-dot combinations: the*Newton's*-*secants*and the Chebyshev's-*secants**methods*and have used the escape time algorithm to analyse the application*of*Julia set theory to these ... Then the efficiency*of*the*Newton's*-*secants**method*will be 3 1/3 1, 442 ... that is between the efficiency*of*the*secants**methods*(1, 61803 ...) and the sufficiency*of*the*Newton's**method*(2 1/2 1, 414 ...##
###
Page 154 of Neural Computation Vol. 4, Issue 2
[page]

1992
*
Neural Computation
*

As a final observation, note that the diagonal

*modification*to the Hes- sian is a sort*of*compromise between gradient descent and*Newton’s**method*: When y tends to zero the original Hessian is (almost) ... Here we follow the terminology*of*Dennis and Schnabel (1983), where the term quasi-Newton refers to all algorithms “derived” from*Newton’s**method*. ...##
###
Page 826 of American Society of Civil Engineers. Collected Journals Vol. 126, Issue 8
[page]

2000
*
American Society of Civil Engineers. Collected Journals
*

One can put the total

*secant**methods*into a form suitable for this style*of*computation with the following*modification*. ... On the other hand, a line search can be used in the modified Newton*method**of*(60), but not in the*secant**method**of*(38) or the damped*secant**method**of*(50). implementation Details As mentioned earlier ...##
###
A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order1+2and Its Dynamics

2015
*
Modelling and Simulation in Engineering
*

A geometric

doi:10.1155/2015/502854
fatcat:tdsjk2hd5regtgm7vxfsoganxi
*modification*to the Newton-*Secant**method*to obtain the root*of*a nonlinear equation is described and analyzed. ... With the same number*of*evaluations, the modified*method*converges faster than*Newton's**method*and the convergence order*of*the new*method*is1+2≈2.4142. ... Many variations*of**Newton's**method*were recently published [4] [5] [6] with different kinds*of**modification*on*Newton's**method*. ...##
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Origin and Evolution of the Secant Method in One Dimension

2013
*
The American mathematical monthly
*

Egyptian Rhind Papyrus, by showing that the Rule

doi:10.4169/amer.math.monthly.120.06.500
fatcat:tw7oj6h6ujhdpozqocnul4qivu
*of*Double False Position coincides with the*secant**method*applied to a linear equation. As such, it predates*Newton's**method*by more than 3,000 years. ... , Regula Falsi*method*, and*secant**method*. ... Jeeves explained that it is "the*secant**modification**of**Newton's**method*". ...##
###
Page 5609 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

*modifications*

*of*the re-cast formula. ... However, in the case

*of*

*Newton’s*

*method*, such an extraneous attracting orbit must have (minimal) period at least 2. ...

##
###
Page 101 of Journal of Spacecraft and Rockets Vol. 14, Issue 2
[page]

1977
*
Journal of Spacecraft and Rockets
*

The relation and near equivalency

*of*the*secant*to*Newton’s**method*is shown. ... Therefore, any*secant*routine with minor logic*modifications*contains a numerical Newton*method*as a special case and hence can be made to approximate the results obtainable with the ‘‘per- turbation*method*...##
###
A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence

2013
*
Advances in Numerical Analysis
*

In most

doi:10.1155/2013/687382
fatcat:vtmghfhstfh4damq32ghyamry4
*of*these cases, hybrids*of*several*methods*such as Newton, bisection, and*secant**methods*are suggested as substitute*methods*and Newton*method*is essentially blended with other*methods*or altogether ... An iterative formula based on*Newton's**method*alone is presented for the iterative solutions*of*equations that ensures convergence in cases where the traditional Newton*Method*may fail to converge to the ...*Secant**method*also fails to converge in several*of*the examples cited in Table 1 : 1 Comparison*of*results*of*iterations*of*the two-point Newton*method*with Newton and*secant**methods*. ...##
###
Fuzzy Version of Secant Method to Solve Fuzzy Non-Linear Equations

2016
*
GANIT Journal of Bangladesh Mathematical Society
*

<p>In this paper fuzzy version

doi:10.3329/ganit.v35i0.28576
fatcat:a2gvspeotbgzrpd2th5gb6iulm
*of**secant**method*has been introduced to obtain approximate solutions*of*a fuzzy non-linear equation. ... The idea*of*converging to the root to the desired degree*of*accuracy, which is the optimum solution,*of*a fuzzy non-linear equation has been focused.</p><p>GANIT J. Bangladesh Math. ... Solving fuzzy non-linear equations over LF *of*the form 0 x f is possible with a*modification**of**Newton's**method*over linear fuzzy real numbers. ...##
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A Two-Point Newton Method suitable for non-convergent Cases and with Super-Quadratic Convergence
[article]

2012
*
arXiv
*
pre-print

In most

arXiv:1210.5766v2
fatcat:x5kspfyu7jefdlnuyhsmru62vq
*of*these cases, hybrids*of*several*methods*such as Newton, bisection and*secant**methods*are suggested as substitute*methods*and Newton*method*is essentially blended with other*methods*or altogether ... In addition, the*method*has super quadratic convergence*of*order 2.414. ...*of**Newton's**method*which leads to an oscillating divergence to infinity. ...##
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A modified secant method for semismooth equations

2003
*
Applied Mathematics Letters
*

A generalization

doi:10.1016/s0893-9659(03)90011-5
fatcat:nfh6tqmc55hnzi2db342nytd7y
*of*the*secant**method*to semismooth equations is proposed. Our goal is to obtain similar convergence as*Newton's**method*, but without evaluating any derivative. ... A*MODIFICATION**OF*THE*SECANT**METHOD*AND CONVERGENCE ANALYSIS The classical*secant**method*can be written as x,+1 = 2, -6F(x,,x,-J'F(x,). ... In thii letter, we analyze a*modification**of*the*secant**method*that requires two function evaluations for step. ...##
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Page 783 of Mathematical Reviews Vol. , Issue 82b
[page]

1982
*
Mathematical Reviews
*

An explicit expression for the estimate

*of*z, is given for the case that N=2, and it is compared with other*methods*(the*secant*rule and*Newton’s**method*). ... M. 82b:65040 A*modification**of*the*secant*rule derived from a maximum likelihood principle. BIT 19 (1979), no. 2, 214-222. ...
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