Construction of Optimal Derivative-Free Techniques without Memory

Algorithm 1

LinearSolve[{{k-x,((k-x)∧2), ((k-x)∧3),((k-x)∧4) } ,

{ y-x, ((y-x)∧2),((y-x)∧3), ((y-x)∧4) } , { z-x, ((z-x)∧2),

((z-x)∧3),((z-x)∧4) } , { w-x, ((w-x)∧2), ((w-x)∧3),((w-x)∧4)}},

{ f[k]-f[x]-r5∗(k-x)∧4,f[y]-f[x]-r5∗(y-x)∧4, f[z]-f[x]

-r5∗(z-x)∧4,f[w]-f[x]-r5∗(w-x)∧4}]//FullSimplify