Ditapis dengan
On modified Newton methods with cubic convergence
Abstract. In this paper, we present two new modified Newton methods for solving a non-linear equation, permitting f'(x) = 0 in some points. These new methods are showed to be cubically convergent. From the practical application, we show that these new methods are vast superior and possible in global convergence. Keywords: Newton method; Third-order convergence; Non-linear equations; Root-f…
- Edisi
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- ISBN/ISSN
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- Deskripsi Fisik
- Applied Mathematics and Computation 176 (2006) 123–127
- Judul Seri
- Applied Mathematics and Computation
- No. Panggil
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A third-order modification of Newton method for systems of non-linear equations
Abstract. In this paper, we present a new modified Newton method for finding a zero of a vector function. It is proved that the order of convergence of the new method is three. This new method permits that the Jacobian is singular in some points. Thus the expected problem, due to the fact the Jacobian is numerically singular, is solved. By numerical examples, we show that this method is vast s…
- Edisi
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- ISBN/ISSN
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- Deskripsi Fisik
- Applied Mathematics and Computation 191 (2007) 117–121
- Judul Seri
- Applied Mathematics and Computation
- No. Panggil
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A modification of Newton method with third-order convergence
Abstract. In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or mo…
- Edisi
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- ISBN/ISSN
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- Deskripsi Fisik
- Applied Mathematics and Computation 181 (2006) 1106–1111
- Judul Seri
- Applied Mathematics and Computation
- No. Panggil
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A family of new Newton-like methods
Abstract. In this paper, we present a family of new Newton-like methods, which removes the severe condition f 0ðxÞ 6¼ 0 in a neighborhood of the required root imposed on Newton’s method. The new methods are quadratically convergent and moreover, have the same error equation as Newton’s method. The detailed analysis of convergence is supplied. The numerical results show that the new meth…
- Edisi
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- ISBN/ISSN
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- Deskripsi Fisik
- Applied Mathematics and Computation 192 (2007) 162–167
- Judul Seri
- Applied Mathematics and Computation
- No. Panggil
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A family of fourth-order methods for solving non-linear equations
Abstract. In this paper, we present a family of new methods with the order of convergence four. Per iteration these methods require two evaluations of the function and one evaluation of its first derivative and therefore this family of methods has the efficiency index equal to 1.587. These methods can be of practical interest, as we show in some examples. Keywords: Newton’s method; Non-l…
- Edisi
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- ISBN/ISSN
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- Deskripsi Fisik
- Applied Mathematics and Computation 188 (2007) 1031–1036
- Judul Seri
- Applied Mathematics and Computation
- No. Panggil
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