Math 781: Homework Assignment # 1due Thursday, 9/4/14Reading1.1, 1.2, 2.1Problems§1.1: 14, 25;§1.2: 7, 10, 16; Problem Plus 1.Problem Plus 1.Define a sequence byx0= 2;xn+1=12xn+1xn∀n >0.It is known thatxn→√2. Prove that the order of the convergence is quadratic.1
Math 781: Homework Assignment # 2due Thursday, 9/11/14Reading2.2Problems§2.1: 1, 4, 9, 13, 14, 16; Problems Plus 1 and 2.Plus 1.Given a general floating point systemσ·(0.a1· · ·an)β·βmwithLmUandβ>1. Find the greatest and smallest positive numbers and the unitroundo↵.Plus 2.(Challenge !!!) In a typical floating point number system a non-zero numberxisstored in the formx=σ·(.a1a2· · ·at)β·βe,whereσ= +1 or-1, 0aiβ-1,t= 53,β= 2, and-1021e1024.(a) Which of the following are numbers in this typical floating point number system ?Explain.