Generalized Newton-Puiseux expansion and Abhyankar-Moh semigroup theorem

We propose a generalized inexact Newton method for solving the inverse eigenvalue problems, which includes the generalized Newton method as a special case. Under the nonsingularity assumption of the Jacobian matrices at the solutionc*, a convergence analysis covering both the distinct and multiple eigenvalue cases is provided and the quadratic convergence property is proved. Moreover, numerical tests are given in the last section and comparisons with the generalized Newton method are made.

Elastohydrodynamic Squeeze Films: Effects of Viscoelasticity and Fluctuating Load

Journal of Lubrication Technology ◽

10.1115/1.3453280 ◽

1979 ◽

Vol 101 (1) ◽

pp. 74-80 ◽

Cited By ~ 12

Author(s):

S. M. Rohde ◽

D. Whicker ◽

J. F. Booker

Keyword(s):

Surface Deformation ◽

Dynamic Responses ◽

Film Rupture ◽

Fully Implicit ◽

Oscillatory Response ◽

Generalized Newton ◽

Newton Scheme ◽

Bounding Surfaces ◽

Implicit Numerical Method ◽

Practical Implications

The dynamic responses of squeeze films to fluctuating loads are compared for the cases of rigid, elastic, and viscoelastic bounding surfaces. Unexpected and interesting differences are observed. These include the oscillatory response of indenter position to a non-negative fluctuating load and the decaying load versus time response to a prescribed indenter trajectory which remains constant over a period of time. Practical implications of these responses are noted. The transient analysis procedure, while general, is applied to a simple geometrical and physical model: an isoviscous Newtonian fluid squeezed between circular, initially flat, three-element viscoelastic Winkler solids. Surface deformation rate and film rupture are incorporated. The fully implicit numerical method utilizes a generalized Newton scheme together with finite element spatial discretization.

Generalized Newton–Raphson algorithm for high dimensional LASSO regression

Statistics and Its Interface ◽

10.4310/20-sii643 ◽

2021 ◽

Vol 14 (3) ◽

pp. 339-350

Author(s):

Yueyong Shi ◽

Jian Huang ◽

Yuling Jiao ◽

Yicheng Kang ◽

Hu Zhang

Keyword(s):

High Dimensional ◽

Lasso Regression ◽

Newton Raphson ◽

Generalized Newton ◽

Raphson Algorithm

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

International Journal of Modern Physics C ◽

10.1142/s0129183195000095 ◽

1995 ◽

Vol 06 (01) ◽

pp. 105-121

Author(s):

MEISHAN ZHAO

Keyword(s):

Angular Momentum ◽

Variational Principle ◽

Total Angular Momentum ◽

Numerical Calculations ◽

Quantum Mechanical ◽

Matrix Elements ◽

Scattering Problems ◽

Identical Particles ◽

Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

Generalized Newton method with applications

Iterative Methods and Their Dynamics with Applications ◽

10.1201/9781315153469-16 ◽

2017 ◽

pp. 259-270

Author(s):

Ioannis K. Argyros ◽

Á. Alberto Magrenan

Keyword(s):

Newton Method ◽

Generalized Newton Method ◽

Generalized Newton

Approximations and generalized Newton methods

Mathematical Programming ◽

10.1007/s10107-017-1194-8 ◽

2017 ◽

Vol 168 (1-2) ◽

pp. 673-716 ◽

Cited By ~ 5

Author(s):

Diethard Klatte ◽

Bernd Kummer

Keyword(s):

Newton Methods ◽

Generalized Newton Methods ◽

Generalized Newton