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I am now reading a journal on how to use haar wavelet method to solve ODEs. I found a difficulties in order to solve below matrix equation. In equation 3, the only unknown matrix isc, how could I factorize this to find^{T}c? (I am using MATLAB in my calculation)^{T}

The matrix equation is :

equation (1) c^{t}[I+4P^{4}]=d^{t}-4f^{T}w^{(3)}(0)P^{3}-4f^{T}w^{(2)}(0)P^{2}-4f^{t}w^{'}(0)P-4f^{T}w(0)

with the boundary conditions

equation (2) w(0)=w^{(2)}(0)=0, w(1)=w^{(2)}(1)=0

by substituting all the boundary conditions, we can gain

equation (3)c^{T}[I+4P^{4}]=d^{T}-4f^{T}[-c^{T}Pf]P^{3}-4f^{T}[-c^{T}P^{3}f+f^{T}(c^{T}Pf)P^{2}f]P

thank you in advance

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# Solving Matrix Equation (factorization)

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