Fourier Matrix Decomposition Methods for the Least Squares Solution of Singular Neumann and Periodic Hermite Bicubic Collocation Problems

1995 ◽  
Vol 16 (2) ◽  
pp. 431-451 ◽  
Author(s):  
Bernard Bialecki ◽  
Karin A. Remington
Keyword(s):  
Least Squares ◽  
Matrix Decomposition ◽  
Decomposition Methods ◽  
Least Squares Solution ◽  
Fourier Matrix

scholarly journals Customized depolarization spatial patterns with dynamic retardance functions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
David Marco ◽  
Guadalupe López-Morales ◽  
María del Mar Sánchez-López ◽  
Ángel Lizana ◽  
Ignacio Moreno ◽  
...  
Keyword(s):  
Spatial Patterns ◽  
Detection System ◽  
Temporal Integration ◽  
Matrix Decomposition ◽  
Decomposition Methods ◽  
Time Dependent ◽  
Light Modulator ◽  
Dynamical Time ◽  
Depolarization Effect ◽  
Spatially Variant

AbstractIn this work we demonstrate customized depolarization spatial patterns by imaging a dynamical time-dependent pixelated retarder. A proof-of-concept of the proposed method is presented, where a liquid–crystal spatial light modulator is used as a spatial retarder that emulates a controlled spatially variant depolarizing sample by addressing a time-dependent phase pattern. We apply an imaging Mueller polarimetric system based on a polarization camera to verify the effective depolarization effect. Experimental validation is provided by temporal integration on the detection system. The effective depolarizance results are fully described within a simple graphical approach which agrees with standard Mueller matrix decomposition methods. The potential of the method is discussed by means of three practical cases, which include non-reported depolarization spatial patterns, including exotic structures as a spirally shaped depolarization pattern.

On the Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Leila Notash
Keyword(s):  
Least Squares ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Constrained Systems ◽  
Solution Set ◽  
Least Squares Solution ◽  
Interval Linear ◽  
Interval Linear Systems ◽  
Parameter Dependency ◽  
Interval Systems

For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized, and implemented to identify the solution set, as well as the minimum 2-norm least-squares solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least-squares solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

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