Abstract: Given a set of measured point correspondences across images and the associated camera projection matrices,the multi-view triangulation refers to the process of estimating the corresponding 3D point.Due to various errors in measured points,an optimality criterion is required for the triangulation.This paper proposes a new optimality criterion which minimizes the L₂-norm distance between the estimated point and the measured point under the constraint that the least singular value of the space plane matrix must be zero.Based on Sampson approximation of the constraint,a simple iterative algorithm is obtained.In addition,by using the conjugate gradient and enforcing the decreasing condition of the least singular value of the space plane matrix in the iterative process,another iterative algorithm with better convergence rate is obtained.Experiments show that our two proposed algorithms both require less number of iterations and have less running time than the Gold Standard algorithm,while yielding comparable estimation accuracy.