Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 13.1, Problem 3CP

Find the point on the hyperbola y = 1 / x closest to the point (2, 3) in two different ways: (a) by Newton’s Method applied to find a critical point (b) by Golden Section Search on the square of the distance between a point on the conic and (2, 3).

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Chapter 13 Solutions

Numerical Analysis

Ch. 13.1 - Prove that the functions are unimodal on some...Ch. 13.1 - Find the absolute minimum in the given intervals...Ch. 13.1 - Plot the function y=f(x) , and find a length-one...Ch. 13.1 - Apply Successive Parabolic Interpolation to the...Ch. 13.1 - Find the point on the hyperbola y=1/x closest to...Ch. 13.1 - Find the point on the ellipse 4x2+9y2=4 farthest...Ch. 13.1 - Prob. 5CPCh. 13.1 - Prob. 6CPCh. 13.1 - Prob. 7CPCh. 13.1 - Prob. 8CP
Ch. 13.2 - Use Newtons Method to find the minimum of...Ch. 13.2 - Prob. 2CPCh. 13.2 - Find the minimum of the Rosenbrock function...Ch. 13.2 - Prob. 4CPCh. 13.2 - Prob. 5CPCh. 13.2 - Prob. 6CP
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