Abdelwahab Kharab's An Introduction to Numerical Methods : A MATLAB Approach, PDF

By Abdelwahab Kharab

ISBN-10: 1439869006

ISBN-13: 9781439869000

Praise for past Editions
Kharab and Guenther provide an enticing, transparent, error-free, and well-written advent to numerical equipment ... hugely recommended.
-J.H. Ellison, CHOICE

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Introduces the speculation and purposes of the main conventional suggestions for fixing numerical difficulties on a working laptop or computer. This paintings covers quite a number helpful algorithms. It incorporates a bankruptcy on Read more...

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

Example text

3 The function f (x) = x3 − x2 − 1 has exactly one zero in [1, 2]. Use the bisection algorithm to approximate the zero of f to within 10−4 . 4) is satisfied. 125. 5]. 609375. 5]. Next we set a2 = c1 and b2 = b1 . 465454. 1. 000122 Solution of x3 − x2 − 1 = 0 in [1, 2] using the bisection method. ✐ ✐ ✐ ✐ ✐ ✐ “k” — 2011/11/22 — 10:14 — page 43 — ✐ THE BISECTION METHOD ✐ 43 Some of the features of MATLAB can be used to view, for example, step-by-step calculations involved in the function bisect.

2 xn . nπ THE METHOD OF FALSE POSITION The method of false position, also known as regula falsi, is similar to the Bisection method but has the advantage of being slightly faster than the latter. As in the bisection method, the function is assumed to be continuous over the interval [x1 , x2 ] with f (x1 )f (x2 ) < 0. 5. From the equation of the secant line, it follows that x3 = x2 − f (x2 ) x2 − x1 . 5 The method of false position and the first two approximations to its zero α. values at which the function changes sign, that is, if f (x1 )f (x3 ) < 0 set x2 = x3 , otherwise set x1 = x3 .

We now introduce some further notation that will be used in this section. , Z. Intervals of the form [a1 , a1 ] are equivalent to the real number a1 . 3 1. A=B If A = [a1 , a2 ], B = [b1 , b2 ] ∈ I ( ), then ⇐⇒ a1 = b1 and a2 = b2 . 2. The absolute value or “magnitude” of A is defined as | A| = max{ | a1 |, | a2 |}. 3. The width of A is defined to be d(A) = a2 − a1 ≥ 0. 4. A partial ordering of the elements of I ( ) is defined by A

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


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