Kinematic Synthesis of Plane Curves

1967 ◽  
Vol 89 (1) ◽  
pp. 173-175 ◽  
Author(s):  
D. W. Lewis ◽  
C. K. Gyory
Keyword(s):  
Least Squares ◽  
Plane Curves ◽  
Kinematic Synthesis ◽  
Point Curve ◽  
Damped Least Squares ◽  
Four Bar Linkage

The coupler point curve of a plane mechanism is a curve that may be described by a series of paired coordinates. An extension of the method of “damped least squares” provides a means for successive adjustment of the parameters which define a particular type mechanism. Repetitive application of this process will result in a convergence toward an optimum approximation to the desired curve as described by the series of paired coordinates. The method has been applied to a four-bar linkage as an example of application.

Displacement and Velocity Kinematic Synthesis

1968 ◽  
Vol 90 (3) ◽  
pp. 527-529 ◽  
Author(s):  
D. W. Lewis ◽  
G. L. Falkenhagen
Keyword(s):  
Least Squares ◽  
Specific Mechanism ◽  
Kinematic Synthesis ◽  
Velocity Transformation ◽  
Data Points ◽  
Damped Least Squares ◽  
Four Bar Linkage

One may wish to define the velocity transformation in addition to the displacement transformation for synthesizing a mechanism. The approach presented here is essentially that noted as the “damped least squares” that allows for successive adjustment of the parameters which define a particular type mechanism. The repetitive application of this process results in a convergence toward an optimum approximation of the displacement and velocity transformation curves which are described by a series of data points. The method has been applied to a four-bar linkage as an example of application; the approach or technique is general and is not limited in use to any specific mechanism.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

Analysis of NMR spectra by damped least squares

1966 ◽  
Vol 21 (1-4) ◽  
pp. 106-107 ◽  
Author(s):  
J. Plíva ◽  
V. Špirko ◽  
S. Toman
Keyword(s):  
Least Squares ◽  
Nmr Spectra ◽  
Damped Least Squares
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