optimal approximation solution
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scholarly journals A Study of Inverse Problems Based on Two Kinds of Special Matrix Equations in Euclidean Space

Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Rui Huang ◽  
Xiaodong Wu ◽  
Ruihe Wang ◽  
Hui Li
Keyword(s):  
Inverse Problems ◽  
Euclidean Space ◽  
Optimal Approximation ◽  
Matrix Equations ◽  
Approximation Solution ◽  
Special Matrix ◽  
Optimal Approximation Solution ◽  
Special Classes

Two special classes of symmetric coefficient matrices were defined based on characteristics matrix; meanwhile, the expressions of the solution to inverse problems are given and the conditions for the solvability of these problems are studied relying on researching. Finally, the optimal approximation solution of these problems is provided.

scholarly journals A class of iteration methods for the matrix equation A×B = C

2007 ◽  
Vol 75 (2) ◽  
pp. 289-298 ◽  
Author(s):  
Konghua Guo ◽  
Xiyan Hu ◽  
Lei Zhang
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Iteration Method ◽  
Optimal Approximation ◽  
Approximation Solution ◽  
Numerical Examples ◽  
The Matrix ◽  
Iteration Methods ◽  
Optimal Approximation Solution

An iteration method for the matrix equation A×B = C is constructed. By this iteration method, the least-norm solution for the matrix equation can be obtained when the matrix equation is consistent and the least-norm least-squares solutions can be obtained when the matrix equation is not consistent. The related optimal approximation solution is obtained by this iteration method. A preconditioned method for improving the iteration rate is put forward. Finally, some numerical examples are given.

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