By Abdelwahab Kharab

ISBN-10: 1439869006

ISBN-13: 9781439869000

**Praise for past Editions**Kharab and Guenther supply an enticing, transparent, error-free, and well-written advent to numerical tools ... hugely recommended.

-J.H. Ellison,

*CHOICE*

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**Read Online or Download An Introduction to Numerical Methods : A MATLAB Approach, Third Edition PDF**

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**Additional resources for An Introduction to Numerical Methods : A MATLAB Approach, Third Edition**

**Example text**

The following MATLAB algorithm computes e−x using a Taylor series expansion: s=1;t=1;i=1; while (abs(t) > eps*abs(s)) .... stop iterating when adding t to s does not change s t=-t*x/i; s=s+t; i=i+1; end result=s Run this algorithm for x=1:20. ✐ ✐ ✐ This page intentionally left blank ✐ ✐ “k” — 2011/11/22 — 10:14 — page 23 — ✐ ✐ Chapter 2 Number System and Errors The way in which numbers are stored and manipulated when arithmetic operations are performed on microcomputers is diﬀerent from the way we, humans, do our arithmetic.

6 Let A = [−1, 2] and B = [1, 3]. The operations mentioned above are now illustrated for these two intervals. [−1, 2] + [1, 3] = [0, 5] [−1, 2] − [1, 3] = [−4, 1] [−1, 2] · [1, 3] = [min{−1, −3, 2, 6}, max{−1, −3, 2, 6}] = [−3, 6] [−1, 2] ÷ [1, 3] = [−1, 2] · [1/3, 1] = [−1, 2]. 4 it is clear that interval arithmetic is an extension of real arithmetic. 4 that the interval addition and interval multiplication are both commutative and associative. That is, if A, B, and C ∈ I ( ), then it follows that A + B = B + A, A · B = B · A, (A + B) + C = A + (B + C), (commutativity) (A · B) · C = A · (B · C).

The emphasis on bracketing the root may sometimes restrict the false position method in diﬃcult situations while solving highly nonlinear equations. 2 1. Verify that the function f (x) = x2 sin x + 2x − 3 has exactly one root in (0, 2). Find this root using the method of false position with an error of no more than 10−3 . 2. Find a root of f (x) = x3 + 2x − 3 in the range 0 ≤ x ≤ 7/5 using the method of false position. 3. 6 has exactly one root in (1, 2). Demonstrate it graphically and determine the root with an error of at most 10−4 using the method of false position.

### An Introduction to Numerical Methods : A MATLAB Approach, Third Edition by Abdelwahab Kharab

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