2) Answer each of the following questions briefly and to the point. What is mean

Question

2) Answer each of the following questions briefly and to the point. What is meant by the machine epsilon? What is the significance of using the machine epsilon as a stopping criterion in an iterative procedure? a) b) Explain why when the series 100,000 n=1 obtained when the series is summed is summed on a digital computer, different results are forwards and backwards. Which result is more accurate? Determine the dimensions of the largest two-dimensional square matrix that can be stored on a digital computer having 1 MB RAM. This array is double precision and each value requires a 64-bit word. Recall that 8 bits 1 byte and 1 kilobyte 210 bytes. c) (cont'd.)

Explanation / Answer

Machine epsilon:

            The gives an higher bound on the relative error due to rounding in floating point arithmetic. These values characterize compute arithmetic in the field of numerical analysis, and by addition in the subject of computational science. The amount is also called unit round off, as well as it has symbols break epsilon

            It is the smallest quantity that is represent able by a computer machine e is defined as the smallest e such that machine knows that 1+E >1 >1-E. machine epsilon provides the spacing between machine represent numbers

            In matlab, the command esp(x) provides the spacing between n and the next machine represent integer

            For x=1,

            Eps(1)

                                    Ans=2.220446049250313e-016

            The computer know that

                                    1+eps(1)=1+220446049250313e-016!=1

            For signal precision, machine epsilon is greater not eps(single(1))

                                    Ans=1.1920929e-007

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.