scholarly journals Discussion: “Matrix Solution for the Vibration of Nonuniform Beams” (Thomson, W. T., 1950, ASME J. Appl. Mech., 17, pp. 337–339)

1951 ◽  
Vol 18 (2) ◽  
pp. 227
Author(s):  
R. M. Rosenberg
Keyword(s):  
Matrix Solution

Comment on the Direct-Matrix Solution of a Singular Lippmann—Schwinger Equation

1973 ◽  
Vol 7 (1) ◽  
pp. 365-367 ◽  
Author(s):  
Eric J. Heller ◽  
William P. Reinhardt
Keyword(s):  
Matrix Solution

scholarly journals An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Zhongli Zhou ◽  
Guangxin Huang
Keyword(s):  
Iterative Algorithm ◽  
Matrix Group ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Matrix Solution ◽  
Initial Matrix ◽  
Special Cases ◽  
Reflexive Matrix ◽  
General Coupled Matrix Equations ◽  
Sylvester Matrix Equations

The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution. When the general coupled matrix equations are consistent over reflexive matrices, the reflexive solution can be determined automatically by the iterative algorithm within finite iterative steps in the absence of round-off errors. The least Frobenius norm reflexive solution of the general coupled matrix equations can be derived when an appropriate initial matrix is chosen. Furthermore, the unique optimal approximation reflexive solution to a given matrix group in Frobenius norm can be derived by finding the least-norm reflexive solution of the corresponding general coupled matrix equations. A numerical example is given to illustrate the effectiveness of the proposed iterative algorithm.

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

Matrix solution of the Bethe-Faddeev equations

1975 ◽  
Vol 11 (1) ◽  
pp. 237-242 ◽  
Author(s):  
Dean W. Halderson ◽  
Paul Goldhammer
Keyword(s):  
Matrix Solution ◽  
Faddeev Equations

Asymptotic Solutions for Mixed-Type Equations with A Small Deviation

1998 ◽  
Vol 5 (2) ◽  
pp. 107-120
Author(s):  
Zhanyuan Hou ◽  
J. S. Cassell
Keyword(s):  
Asymptotic Behavior ◽  
Mixed Type ◽  
Small Deviation ◽  
Asymptotic Solutions ◽  
Sufficient Condition ◽  
Single Variable ◽  
Bounded Solutions ◽  
Matrix Solution ◽  
Linear Vector

Abstract An asymptotic matrix solution is formulated for a class of mixed-type linear vector equations with a single variable deviation which is small at infinity. This matrix solution describes the asymptotic behavior of all exponentially bounded solutions. A sufficient condition is obtained for there to be no other solutions.

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