GEOE 359 Lecture Notes - Lecture 4: Round-Off Error, Numerical Error, Significant Figures

• School: Queen's University
• Department: Geological Engineering Courses
• Course: GEOE 359
• Professor: Georgia Fotopoulos

Document Summary

Due to the li(cid:373)ited (cid:271)its availa(cid:271)le i(cid:374) a (cid:272)o(cid:373)puter to store (cid:374)u(cid:373)(cid:271)ers, (cid:858)lo(cid:374)ger(cid:859) (cid:374)u(cid:373)(cid:271)ers (cid:374)eed to (cid:271)e shortened by rounding or chopping them in order to fit resulting in a round-off error ero. Round-off errors occur when: subtracting two nearly identical numbers, when two vastly different numbers are involved in a calculation. Are the reason for resulting in loss of significance/precision. The difference between the truce solution x and the solution calculated by specific approximate mathematical algorithm employed to solve the problem. It always includes round-off errors and depending on the numerical method it can also include truncation errors. Together the round-off and truncation errors yield the total numerical error that is included in the numerical solution. Total error (also called true error) is difference between the true (exact) solution and the numerical solution (true error = true solution numerical solution)