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Table 1 Results for Example 5.3 using the algorithm in Corollary 3.4

From: Gradient projection method with a new step size for the split feasibility problem

Choiceness u Starting points \(x_{0}\) Number of iterations CPU (s) Approximate solution \(x^{*}\) (approximates of \(Ax^{*}\) and \(\|x^{*}\|_{2}\))
\((0,0,0,0)^{T}\) \((0,0,0,0)^{T}\) 9500 5.317 \((1.974662,0.512779,-0.498849,-0.508389)^{T}\)
\((0,0,0,0)^{T}\) \((1,1,1,1)^{T}\) 9501 5.187 \((1.974695,0.512718,-0.498837,-0.508336)^{T}\)
\((0,0,0,0)^{T}\) \((1,2,3,4)^{T}\) 9505 5.217 \((1.974803,0.512523,-0.498798,-0.508168)^{T}\)
     \(Ax^{*} = (0.99528,1.97981,2.97675)^{T}\), \(\|x^{*}\|_{2} = 2.16091\)
\((1,1,1,1)^{T}\) \((0,0,0,0)^{T}\) 9406 5.488 \((2.130245,0.226710,-0.439453,-0.255758)^{T}\)
\((1,1,1,1)^{T}\) \((1,1,1,1)^{T}\) 9406 5.888 \((2.130278,0.226649,-0.439440,-0.255705)^{T}\)
\((1,1,1,1)^{T}\) \((1,2,3,4)^{T}\) 9409 5.568 \((2.130386,0.226451,-0.439402,-0.255534)^{T}\)
     \(Ax^{*} = (1.00955,1.97560,2.98010)^{T}\), \(\|x^{*}\|_{2} = 2.20179\)
\((1,2,3,4)^{T}\) \((0,0,0,0)^{T}\) 12,180 4.977 \((2.641308,-0.734424,-0.244857,0.583179)^{T}\)
\((1,2,3,4)^{T}\) \((1,1,1,1)^{T}\) 12,179 5.127 \((2.641332,-0.734471,-0.244847,0.583221)^{T}\)
\((1,2,3,4)^{T}\) \((1,2,3,4)^{T}\) 12,178 5.387 \((2.641411,-0.734620,-0.244817,0.583350)^{T}\)
     \(Ax^{*} = (1.02107,1.96452,2.97978)^{T}\), \(\|x^{*}\|_{2} = 2.81353\)