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### Secant modification of Newton's method

T. A. Jeeves
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.  ...

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

Juhari Juhari
2021 CAUCHY
The obtained results from the analysis 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.  ...

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

Anna Tomova
2001 International Journal of Mathematics and Mathematical Sciences
It is known that the application 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

Gustavo Fernández-Torres
2015 Modelling and Simulation in Engineering
A geometric 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    with different kinds of modification on Newton's method.  ...

### Origin and Evolution of the Secant Method in One Dimension

Joanna M. Papakonstantinou, Richard A. Tapia
2013 The American mathematical monthly
Egyptian Rhind Papyrus, by showing that the Rule 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

Ababu Teklemariam Tiruneh, W. N. Ndlela, S. J. Nkambule
In most 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

Goutam Kumar Saha, Shapla Shirin
2016 GANIT Journal of Bangladesh Mathematical Society
<p>In this paper fuzzy version 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.  ...

### A Two-Point Newton Method suitable for non-convergent Cases and with Super-Quadratic Convergence [article]

Ababu Teklemariam Tiruneh
2012 arXiv   pre-print
In most 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.  ...

### A modified secant method for semismooth equations

S. Amat, S. Busquier
2003 Applied Mathematics Letters
A generalization 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.  ...

### 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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