CS 205A hw1

# Scientific Computing

• Homework Help
• PresidentHackerCaribou10582
• 2

This preview shows pages 1–2. Sign up to view the full content.

CS205 Homework #1 Problem 1 Arithmetic operations are subject to roundoff error when performed on a finite precision computer. In order to perform an operation x op y on the real numbers x and y we deviate from the analytic result when discretizing those values to machine precision as well as when we store the resulting value. Let ¯ x denote the discretized, floating point version of x that is stored on the computer. You may assume that ¯ x = (1 + ) x where is bounded as 0 ≤ | | < max where max 1 is the machine roundoff precision. Assume that the result of the arithmetic operation between two floating point numbers ¯ x and ¯ y is computed exactly, but when stored on the computer it is once again subject to roundoff error as x op y = (1 + )( x op y ) where the roundoff error obeys the same bounds 0 ≤ | | < max . The relative error of a computation is defined as E = Computed Result - Analytic Result Analytic Result Provide a bound (in terms of max ) for the relative error induced by the following arith- metic operations, or prove that the relative error is unbounded.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern