In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate ...In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.展开更多
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw...We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.展开更多
In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the ...In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.展开更多
This paper gives the extension of Newton’s method, and a variety of formulas to compare the convergences for the extension of Newton’s method (Section 4). Section 5 gives the numerical calculations. Section 1 introd...This paper gives the extension of Newton’s method, and a variety of formulas to compare the convergences for the extension of Newton’s method (Section 4). Section 5 gives the numerical calculations. Section 1 introduces the three formulas obtained from the cubic equation of a hearth by Murase (Ref. [1]). We find that Murase’s three formulas lead to a Horner’s method (Ref. [2]) and extension of a Newton’s method (2009) at the same time. This shows originality of Wasan (mathematics developed in Japan) in the Edo era (1603-1868). Suzuki (Ref. [3]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 2 gives the relations between Newton’s method, Horner’s method and Murase’s three formulas. Section 3 gives a new function defined such as .展开更多
We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algo...We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.展开更多
In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2...In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.展开更多
In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis...In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis function sets of these polynomialinterpolation methods are given. An example also shows the effectiveness of the results.展开更多
The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s met...The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.展开更多
为了提高CMAC(cerebellar model articulation controller)神经网络实时在线学习的快速性和准确性,在基于信度分配的CA-CMAC-AMS学习算法的基础上,结合牛顿向前插公式,提出了一种新的CMAC-AMS学习算法(CA-NCMAC-AMS)。数值模拟表明,这种...为了提高CMAC(cerebellar model articulation controller)神经网络实时在线学习的快速性和准确性,在基于信度分配的CA-CMAC-AMS学习算法的基础上,结合牛顿向前插公式,提出了一种新的CMAC-AMS学习算法(CA-NCMAC-AMS)。数值模拟表明,这种CA-NCMAC-AMS的学习算法不但有较快的学习速度和训练精度及建模能力,而且在信号处理、模式识别及高精度的实时智能控制等领域具有很大的应用潜力。展开更多
文摘In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.
文摘We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.
文摘In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.
文摘This paper gives the extension of Newton’s method, and a variety of formulas to compare the convergences for the extension of Newton’s method (Section 4). Section 5 gives the numerical calculations. Section 1 introduces the three formulas obtained from the cubic equation of a hearth by Murase (Ref. [1]). We find that Murase’s three formulas lead to a Horner’s method (Ref. [2]) and extension of a Newton’s method (2009) at the same time. This shows originality of Wasan (mathematics developed in Japan) in the Edo era (1603-1868). Suzuki (Ref. [3]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 2 gives the relations between Newton’s method, Horner’s method and Murase’s three formulas. Section 3 gives a new function defined such as .
基金This paper is a talk on the held in Nanjing, P. R. China, July, 2004.
文摘We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.
文摘In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.
文摘In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis function sets of these polynomialinterpolation methods are given. An example also shows the effectiveness of the results.
文摘The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.
文摘为了提高CMAC(cerebellar model articulation controller)神经网络实时在线学习的快速性和准确性,在基于信度分配的CA-CMAC-AMS学习算法的基础上,结合牛顿向前插公式,提出了一种新的CMAC-AMS学习算法(CA-NCMAC-AMS)。数值模拟表明,这种CA-NCMAC-AMS的学习算法不但有较快的学习速度和训练精度及建模能力,而且在信号处理、模式识别及高精度的实时智能控制等领域具有很大的应用潜力。
