Historical Development of the Newton–Raphson Method

Ypma, Tjalling

doi:10.1137/1037125

Cited by 726 publications

(298 citation statements)

References 8 publications

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“…We assigned the model parameters as discussed above, and the cell diameters were computed from equations (3.2) -(3.3) numerically, using the Newton -Raphson scheme [29]. Sensitivities of the model to our assumptions were computed numerically using equations (3.8) -(3.11).…”

Section: Implementation Of the Methodsmentioning

confidence: 99%

Retrieval of phytoplankton size from bio-optical measurements: theory and applications

Roy

Sathyendranath

Platt

2010

J. R. Soc. Interface.

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The absorption coefficient of a substance distributed as discrete particles in suspension is less than that of the same material dissolved uniformly in a medium-a phenomenon commonly referred to as the flattening effect. The decrease in the absorption coefficient owing to flattening effect depends on the concentration of the absorbing pigment inside the particle, the specific absorption coefficient of the pigment within the particle, and on the diameter of the particle, if the particles are assumed to be spherical. For phytoplankton cells in the ocean, with diameters ranging from less than 1 mm to more than 100 mm, the flattening effect is variable, and sometimes pronounced, as has been well documented in the literature. Here, we demonstrate how the in vivo absorption coefficient of phytoplankton cells per unit concentration of its major pigment, chlorophyll a, can be used to determine the average cell size of the phytoplankton population. Sensitivity analyses are carried out to evaluate the errors in the estimated diameter owing to potential errors in the model assumptions. Cell sizes computed for field samples using the model are compared qualitatively with indirect estimates of size classes derived from high performance liquid chromatography data. Also, the results are compared quantitatively against measurements of cell size in laboratory cultures. The method developed is easy-to-apply as an operational tool for in situ observations, and has the potential for application to remote sensing of ocean colour data.

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Section: Implementation Of the Methodsmentioning

confidence: 99%

Retrieval of phytoplankton size from bio-optical measurements: theory and applications

Roy

Sathyendranath

Platt

2010

J. R. Soc. Interface.

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“…The window variations performed by Newton Raphson method [18] are taken from the section 2 (12) analytical identity which includes non linear variation of x (τ). The term Δf t indicates the bandwidth of the guassian function and…”

Section: Physical Methods For Proposed Algorithmmentioning

confidence: 99%

Time Frequency analysis of Non-Stationary signals by Differential frequency window S –Transform

Krishna¹,

Srinivas²,

Gopal³

et al. 2018

IJET

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The S transform is an extension of Short Time Fourier Transform and Wavelet transform, has a time frequency resolution which is far from ideal. A differential frequency window is proposed in this paper to enhance the time frequency energy localization. When a non stationary signal consists of abrupt amplitude variation equal to peak of Gaussian function at initial intervals of chosen guassian window, then some part of the signal amplitude will be nullified during transform projection. The major function of differential frequency window is to track all abrupt amplitude-frequency variations which exploits in non -stationary signals. A mathematical method namely Newton Raphson method is adopted for this trace. The proposed scheme is tested for ECG data in presence of noise environment and results shows that proposed algorithm produces better enhanced energy localization in comparison to the standard S -Transform, STFT, and CWT. Furthermore the above algorithm is implemented on FPGA for real time applications.

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“…The SCARA robot is here used only as a test. Classical numerical methods, considered in this paper, consist on linearizing the inverse kinematic equations, setting up an initial position and then using Newton's method, a generalization of Newton's method or another iterative methods [49][50][51]. Numerical methods can be applied to analyze any manipulator topology, but they can be affected by uncertainty in obtaining all possible solutions [52].…”

Section: Matec Web Of Conferencesmentioning

confidence: 99%

Inverse Kinematics of a Serial Robot

Amici

Cappellini

2016

MATEC Web of Conferences

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Abstract. This work describes a technique to treat the inverse kinematics of a serial manipulator. The inverse kinematics is obtained through the numerical inversion of the Jacobian matrix, that represents the equation of motion of the manipulator. The inversion is affected by numerical errors and, in different conditions, due to the numerical nature of the solver, it does not converge to a reasonable solution. Thus a soft computing approach is adopted to mix different traditional methods to obtain an increment of algorithmic convergence.

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Historical Development of the Newton–Raphson Method

Cited by 726 publications

References 8 publications

Retrieval of phytoplankton size from bio-optical measurements: theory and applications

Retrieval of phytoplankton size from bio-optical measurements: theory and applications

Time Frequency analysis of Non-Stationary signals by Differential frequency window S –Transform

Inverse Kinematics of a Serial Robot

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