A novel algorithm to solve dwell time based on linear algebra (matrix-based algorithm) is discussed

in which math model changes the fabrication process from convolution to matrix product

so that the calculation of the dwell time becomes a solution to linear equations. Traditional factorization methods such as Gaussian elimination and total least squares can not be used because the linear equations are severely ill condition. So

the Tikhonov regularization is used to solve the ill-posed problem caused by meterage error

and the regularization parameter is determined adaptive method without any prior knowledge. By comparing with different algorithms

the advantages of the matrix-based algorithm are obviously with the precision enhancing 30%. In the end

an error data is solved with actual parameters using the matrix-based algorithm. The simulation results show that the convergence rates of the PV and RMS values can reach up to 0.48 and 0.62

respectively. The matrix-based algorithm can satisfy the requirement of fabrication very well.