Algorithm A1 Algorithm for resizing an image

1: for $x=1$ to image width in pixels do 2:  for $y=1$ to image height in pixels do 3:   Arrange augmented y matrix using the weights from the referenced equations: $$\left[\begin{array}{cccc}1& y_1& y_1^2& y_1^3\\ 1& y_2& y_2^2& y_2^3\\ 1& y_3& y_3^2& y_3^3\\ 1& y_4& y_4^2& y_4^3\end{array}\right]\left[\begin{array}{c}{W}_{-1}\left(S_y\right)\\ W_0\left(S_y\right)\\ W_1\left(S_y\right)\\ W_2\left(S_y\right)\end{array}\right]$$                 ▹W are the weight functions and $S_y$ is the scaling factor in y direction. 4:   Apply the Gauss Jordan elimination method to solve for p values by Equation (A7): $$p=W_{-1}\left(S_y\right)f_{i-1,j}+W_0\left(S_y\right)f_{i,j}+W_1\left(S_y\right)f_{i+1,j}+W_2\left(S_y\right)f_{i+2,j}$$ 5:   Enter the y value of the pixels 6:   Arrange augmented x matrix using the weights from the referenced equations: $$\left[\begin{array}{cccc}1& x_1& x_1^2& x_1^3\\ 1& x_2& x_2^2& x_2^3\\ 1& x_3& x_3^2& x_3^3\\ 1& x_4& x_4^2& x_4^3\end{array}\right]\left[\begin{array}{c}{W}_{-1}\left(S_x\right)\\ W_0\left(S_x\right)\\ W_1\left(S_x\right)\\ W_2\left(S_x\right)\end{array}\right]$$                 ▹W are the weight functions and $S_x$ is the scaling factor in x direction. 7:   Apply the Gauss Jordan elimination method to solve for p values by Equation (A9): $$p=W_{-1}\left(S_x\right)f_{i,j-1}+W_0\left(S_x\right)f_{i,j}+W_1\left(S_x\right)f_{i,j+1}+W_2\left(S_x\right)f_{i,j+2}$$ 8:   Enter the x value of the pixels to searched equation 9:  end for 10: end for 11: Perform rounding on each pixel value