Exact inverse solution techniques for a class of complex valued block two-by-two linear systems

2021 ◽  
Author(s):  
Zhao-Zheng Liang ◽  
Owe Axelsson
Keyword(s):  
Linear Systems ◽  
Inverse Solution ◽  
Complex Valued ◽  
Solution Techniques

scholarly journals Almost block diagonal linear systems: sequential and parallel solution techniques, and applications

2000 ◽  
Vol 7 (5) ◽  
pp. 275-317 ◽  
Author(s):  
P. Amodio ◽  
J. R. Cash ◽  
G. Roussos ◽  
R. W. Wright ◽  
G. Fairweather ◽  
...  
Keyword(s):  
Linear Systems ◽  
Parallel Solution ◽  
Block Diagonal ◽  
Solution Techniques

Bounds for the characteristic exponents of linear systems

1965 ◽  
Vol 61 (4) ◽  
pp. 889-894 ◽  
Author(s):  
R. A. Smith
Keyword(s):  
Differential Equations ◽  
Linear Systems ◽  
Characteristic Exponent ◽  
Zero Solution ◽  
System Of Differential Equations ◽  
Characteristic Exponents ◽  
Integrable Functions ◽  
Image Position ◽  
Complex Valued

For an n-vector x = (xi) and n × n matrix A = (aij) with complex elements, let |x|2 = Σi|xi|2,|A|2 = ΣiΣj|aij|2. Also, M(A), m(A) denoteℜλ1,ℜλn, respectively, where λ1,…,λA are the eigenvalues of A arranged so that ℜλ1 ≥ … ≥ ℜλn. Throughout this paper A(t) denotes a matrix whose elements aij(t) are complex valued Lebesgue integrable functions of t in (0, T) for all T > 0. Then M(A(t)), m(A(t)) are also Lebesgue integrable in (0, T) for all T > 0. The characteristic exponent μ of a non-zero solution x(t) of the n × n system of differential equationscan be defined, following Perron ((12)), aswhere ℒ denotes lim sup as t → + ∞. When |A(t)| is bounded in (0,∞), μ is finite; in other cases it could be ± ∞.

Inverse Kinematics Solutions for General Spatial Linkages

1987 ◽  
Author(s):  
M. Tucker ◽  
N. D. Perreira
Keyword(s):  
Inverse Kinematics ◽  
Robot Control ◽  
Degrees Of Freedom ◽  
General Purpose ◽  
Inverse Solution ◽  
Six Degrees Of Freedom ◽  
Inverse Kinematics Problem ◽  
Spatial Linkages ◽  
Pseudo Inverse ◽  
Solution Techniques

Abstract A procedure for obtaining solutions to the general inverse kinematics problem for both position and velocity is presented. Solutions to this problem are required for improved robot control and linkage synthesis. The procedure requires obtaining the inverse of the actual robot linkage Jacobian. A procedure to detect the presence of singularities in the Jacobians and their causes are given. Inverse solution techniques applicable to robots with less than, equal to, or greater than six degrees of freedom and their implementation to robots with various types of singularities is outlined. For each case, the implementation of both the complete Moore-Penrose inverse and a robot specific pseudo inverse are included. Although it is not necessary to use the complete Moore-Penrose inverse on any particular robot, it can be used to obtain generic inverse routines for general purpose applications.

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