One-Dimensional Optimization 3-Spline Interpolation Method And Minimum E₁-norm Solution Of Accelerated Projected Gradient Method

This paper firstly discusses that using 3-spline interpolation function approxi-mates object function,we get iteration formulas In this article,this iteration formulas’convergence and convergence rate are dis-cussed in detail. Then discuss accelerating proj ection gradient algorithm x(n+1)=PR(x(n)+β(n)K*(y-Kx(n)). It produces points column{xn}:However,when x0 changes,The cluster point of{xn} will change.Therefore,this algorithm can get not l1一norm least solution.This is exactly what we in this paper to solve the problem.