A modification of the numerical integration error method for the zero-finding problem of an analytic function

2005 ◽  
Vol 22 (3) ◽  
pp. 353-365 ◽  
Author(s):  
Tomohiro Suzuki ◽  
Toshio Suzuki
Keyword(s):  
Analytic Function ◽  
Numerical Integration ◽  
Integration Error ◽  
Numerical Integration Error ◽  
Error Method

Numerical integration error method – a new method for polynomial root-finding

2001 ◽  
Vol 47 (6) ◽  
pp. 3859-3868 ◽  
Author(s):  
Tomohiro Suzuki ◽  
Toshio Suzuki
Keyword(s):  
Numerical Integration ◽  
New Method ◽  
Root Finding ◽  
Integration Error ◽  
Numerical Integration Error ◽  
Polynomial Root Finding ◽  
Error Method

scholarly journals Improved Calibration of Numerical Integration Error in Sigma-Point Filters

2020 ◽  
pp. 1-1
Author(s):  
Jakub Pruher ◽  
Toni Karvonen ◽  
Christopher James Oates ◽  
Ondrej Straka ◽  
Simo Sarkka
Keyword(s):  
Numerical Integration ◽  
Sigma Point ◽  
Integration Error ◽  
Numerical Integration Error

scholarly journals Behavior of the Numerical Integration Error

2014 ◽  
Vol 05 (10) ◽  
pp. 1412-1426
Author(s):  
Tchavdar Marinov ◽  
Joe Omojola ◽  
Quintel Washington ◽  
LaQunia Banks
Keyword(s):  
Numerical Integration ◽  
Integration Error ◽  
Numerical Integration Error

scholarly journals Numerical Integration of Analytic Function Through Extrapolation

2017 ◽  
Vol 10 (37) ◽  
pp. 1-8
Author(s):  
Arjun Singh ◽  
Saumya Ranjan Jena ◽  
Bhupati B. Mishra ◽  
◽  
◽  
...  
Keyword(s):  
Analytic Function ◽  
Numerical Integration

Canonical Impulse-Momentum Equations for Impact Analysis of Multibody Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 180-186 ◽  
Author(s):  
H. M. Lankarani ◽  
P. E. Nikravesh
Keyword(s):  
Differential Equations ◽  
Numerical Integration ◽  
Canonical Form ◽  
Multibody Systems ◽  
Impact Analysis ◽  
Equations Of Motion ◽  
Momentum Balance ◽  
Constraint Violation ◽  
Numerical Integration Error ◽  
Intermittent Motion

For mechanical systems that undergo intermittent motion, the usual formulation of the equations of motion is not valid over the periods of discontinuity, and a procedure for balancing the momenta of these systems is often performed. A canonical form of the equations of motion is used here as the differential equations of motion. A set of momentum balance-impulse equations is derived in terms of a system total momenta by explicitly integrating the canonical equations. The method is stable when the canonical equations are numerically integrated and it is efficient when the derived momentum balance-impulse equations are solved. The method shows that the constraint violation phenomenon, which is usually caused by the numerical integration error, can be substantially reduced as compared to the numerical integration of the standard Newtonian form of equations of motion. Examples are provided to illustrate the validity of the method.

scholarly journals Accurate Computation of Fractional-Order Exponential Moments

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Shujiang Xu ◽  
Qixian Hao ◽  
Bin Ma ◽  
Chunpeng Wang ◽  
Jian Li
Keyword(s):  
Numerical Integration ◽  
Fractional Order ◽  
Numerical Instability ◽  
Calculation Methods ◽  
Image Description ◽  
Accurate Calculation ◽  
Orthogonal Moments ◽  
Instability Problem ◽  
Exponential Moments ◽  
Numerical Integration Error

Exponential moments (EMs) are important radial orthogonal moments, which have good image description ability and have less information redundancy compared with other orthogonal moments. Therefore, it has been used in various fields of image processing in recent years. However, EMs can only take integer order, which limits their reconstruction and antinoising attack performances. The promotion of fractional-order exponential moments (FrEMs) effectively alleviates the numerical instability problem of EMs; however, the numerical integration errors generated by the traditional calculation methods of FrEMs still affect the accuracy of FrEMs. Therefore, the Gaussian numerical integration (GNI) is used in this paper to propose an accurate calculation method of FrEMs, which effectively alleviates the numerical integration error. Extensive experiments are carried out in this paper to prove that the GNI method can significantly improve the performance of FrEMs in many aspects.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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