due 22 January 2014 in class

Read chapter 4 in the book by Higham & Higham, as well as the IEEE Standard for Binary Floating Point Arithmetic.

Try out Cleve Moler's Matlab program floatgui.m.

- The program shows you the spacing of floating point numbers.
The parameter t specifies the number of bits in the fraction, and the
parameters e

- [10 points] Let A be a mxn matrix, and e the nx1 vector of all ones. What does the matrix vector product Ae do?
- [10 points] Characterize the class of unitary, Hermitian positive definite matrices. Prove your answer.
- [10 points] The expressions 2^(-1024) and 1/(2^1024) are equal in exact arithmetic. Explain what happens when they are evaluated in IEEE double precision arithmetic, and why.
- [10 points]
Determine the
*exact values*of x and xp1, in terms of powers of two, at the termination of the Matlab algorithm below. Explain the purpose of the algorithm.x = 1; xp1 = x + 1; while xp1 > 1 x = x/2; xp1 = x + 1; end x = 2*x;