2. Let X1, X2, ... be a sequence of floating point numbers, and let Sn = x1 + ... + In. Consider Kahan's compensated summation algorithm Yn = Xn + en-1 n = $n-1 + yn en = = (n-1 n) + yn, n=1,2,... where each operation is performed in floating point arithmetic, and o = eo = 0. Show that n sn] = [C + 0(22)]\xkl, n k=1 where C is some constant, and is the machine precision. 2. Let X1, X2, ... be a sequence of floating point numbers, and let Sn = x1 + ... + In. Consider Kahan's compensated summation algorithm Yn = Xn + en-1 n = $n-1 + yn en = = (n-1 n) + yn, n=1,2,... where each operation is performed in floating point arithmetic, and o = eo = 0. Show that n sn] = [C + 0(22)]\xkl, n k=1 where C is some constant, and is the machine precision