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The least-squares solutions of the matrix equations AXB+CYD=Hand AXB+CXD=H for symmetric arrowhead matrices are discussed. By using the Kronecker product and stretching function of matrices, the explicit representations of the general solution are given. Also, it is shown that the best approximation solution is unique and an explicit expression of the solution is derived

journal of applied mathematics

Least-Squares Solutions of the Matrix Equations<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:mi>Y</mml:mi><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mi>H</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:mi>X</mml:mi><mml:mi>D</mml:mi><mml:mo>=</mml:mo><…

Least-Squares Solutions of the Matrix EquationsAXB+CYD=HandAXB+CXD=<…