Exploration 2.2.11 h MATLAB, generate three random numbers r, y and z, and com-

Question

Exploration 2.2.11 h MATLAB, generate three random numbers r, y and z, and com- pute r + (y 2) and (r + y) + =. Do they agree? Try this a few times with different random numbers and observe what happens. What would have to be true of r, y and to cause a significant deviation? 2.2.2.3 Overflow and Underflow Furthermore, overflow or underflow may occur depending on the exponents of the operands, since their sum or difference may lie outside of the interval [L.U Exploration 2.2.12 Consider the formula : Vp+1, Erplain how overflow can occur in computing : , even if, y and all have magnitudes that can be represented How can this formula be reuritten so that overflow does not occur? Exploration 2.2.13 Let x R Use the result of Erploation 22.19 to describe an algorithm for computing 1/2 in such a way as to prevent overflow. 2.2.2.4 Cancellation Subtraction of floating-point numbers presents a unique difficulty, in addition to the rounding error previously discussed. Exploration 2.2.14 When performing the subtraction 0.345769258233 -0.345769258174 being subtracted have p significant digits, and the first (most stgnficant, or left to right) m digits agree, how many significant digits, at most, can the result have?

Explanation / Answer

while performing the subraction for the given values,

                        0.345769258233

                      - 0.345769258174

                   ----------------------------------

                        0.000000000059

the most significant digit is 0.000000000059

the result can have atmost 1 significant digit

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