Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 3.3, Problem 1E

List the Chebyshev interpolation nodes x 1 , ... , x n in the given interval. (a) [ − 1 , 1 ] , n = 6 ( b ) [ − 2 , 2 ] , n = 4 ( c ) [ 4 , 12 ] , n = 6 ( d ) [ − 0.3 , 0.7 ] , n = 5

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Chapter 3 Solutions

Numerical Analysis

Ch. 3.1 - Use Lagrange interpolation to find a polynomial...Ch. 3.1 - Use Newtons divided differences to find the...Ch. 3.1 - How many degree d polynomials pass through the...Ch. 3.1 - (a) Find a polynomial P(x) of degree 3 or less...Ch. 3.1 - (a) Find a polynomial P(x) of degree 3 or less...Ch. 3.1 - Write down a polynomial of degree exactly 5 that...Ch. 3.1 - Find P(0), where P(x) is the degree 10 polynomial...Ch. 3.1 - Let P(x) be the degree 9 polynomial that takes the...Ch. 3.1 - Give an example of the following, or explain why...Ch. 3.1 - Let P(x) be the degree 5 polynomial that takes the...
Ch. 3.1 - Let P1, P2, P3, and P4 be four different points...Ch. 3.1 - Can a degree 3 polynomial intersect a degree 4...Ch. 3.1 - Let P(x) be the degree 10 polynomial through the...Ch. 3.1 - Write down 4 noncollinear points (1,y1), (2,y2),...Ch. 3.1 - Write down the degree 25 polynomial that passes...Ch. 3.1 - List all degree 42 polynomials that pass through...Ch. 3.1 - The estimated mean atmospheric concentration of...Ch. 3.1 - Prob. 18ECh. 3.1 - Apply the following world population figures to...Ch. 3.1 - Write a version of Program 3.2 that is a MATLAB...Ch. 3.1 - Write a MATLAB function polyinterp.m that takes as...Ch. 3.1 - Remodel the sin1 calculator key in Program 3.3 to...Ch. 3.1 - (a) Use the addition formulas for sin and cos to...Ch. 3.2 - Find the degree 2 interpolating polynomial P2(x)...Ch. 3.2 - (a) Given the data points (1,0), (2,In2), (4,In4),...Ch. 3.2 - Assume that the polynomial P9(x) interpolates the...Ch. 3.2 - Consider the interpolating polynomial for...Ch. 3.2 - Assume that a function f(x) has been approximated...Ch. 3.2 - Assume that the polynomial P5(x) interpolates a...Ch. 3.2 - (a) Use the method of divided differences to find...Ch. 3.2 - Plot the interpolation error of the sin1 key from...Ch. 3.2 - The total world oil production in millions of...Ch. 3.2 - Use the degree 3 polynomial through the first four...Ch. 3.3 - List the Chebyshev interpolation nodes x1,...,xn...Ch. 3.3 - Find the upper bound for | (xx1)...(xxn) | on the...Ch. 3.3 - Assume that Chebyshev interpolation is used to...Ch. 3.3 - Answer the same questions as in Exercise 3, but...Ch. 3.3 - Find an upper bound for the error on [ 0,2 ] when...Ch. 3.3 - Assume that you are to use Chebyshev interpolation...Ch. 3.3 - Suppose you are designing the In key for a...Ch. 3.3 - Let Tn(x) denote the degree n Chebyshev...Ch. 3.3 - Determine the following values: (a) T999(1) (b)...Ch. 3.3 - Prob. 1CPCh. 3.3 - Prob. 2CPCh. 3.3 - Carry out the steps of Computer Problem 2 forIn x,...Ch. 3.3 - Let f(x)=e| x |, Compare evenly spaced...Ch. 3.3 - Prob. 5CPCh. 3.4 - Decide whether the equations form a cubic spline....Ch. 3.4 - Check the spline conditions for {...Ch. 3.4 - Find c in the following cubic splines. Which of...Ch. 3.4 - Find k1,k2,k3 in the following cubic spline. Which...Ch. 3.4 - How many natural cubic splines on [ 0,2 ] are...Ch. 3.4 - Find the parabolically terminated cubic spline...Ch. 3.4 - Solve equations 3.26 to find the natural cubic...Ch. 3.4 - Solve equations 3.26 to find the natural cubic...Ch. 3.4 - Prob. 9ECh. 3.4 - True or false: Given n=3 data points, the...Ch. 3.4 - (a) How many parabolically terminated cubic...Ch. 3.4 - How many not-a-knot cubic splines are there for...Ch. 3.4 - Find b1 and c3 in the cubic spline S(x)={...Ch. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Discuss the existence and uniqueness of a...Ch. 3.4 - Prob. 21ECh. 3.4 - Prob. 1CPCh. 3.4 - Find and plot the not-a-knot cubic spline that...Ch. 3.4 - Find and plot the cubic spline S satisfying...Ch. 3.4 - Prob. 4CPCh. 3.4 - Prob. 5CPCh. 3.4 - Find and plot the cubic spline S satisfying...Ch. 3.4 - Prob. 7CPCh. 3.4 - Prob. 8CPCh. 3.4 - Find the clamped cubic spline that interpolates...Ch. 3.4 - Find the number of interpolation nodes in Computer...Ch. 3.4 - (a) Consider the natural cubic spline through the...Ch. 3.4 - Prob. 12CPCh. 3.4 - In a single plot, show the natural, not-a-knot,...Ch. 3.4 - Prob. 14CPCh. 3.4 - Prob. 15CPCh. 3.5 - Find the one-piece BĂ©zier curve (x(t),y(t))...Ch. 3.5 - Find the first endpoint two control points, and...Ch. 3.5 - Find the three-piece BĂ©zier curve forming the...Ch. 3.5 - Build a four-piece BĂ©zier spline that forms a...Ch. 3.5 - Describe the character drawn by the following...Ch. 3.5 - Describe the character drawn by the following...Ch. 3.5 - Find a one-piece BĂ©zier spline that has vertical...Ch. 3.5 - Find a one-piece Bezier spline that has a...Ch. 3.5 - Prob. 9ECh. 3.5 - Find the knots and control points for the...Ch. 3.5 - Prove the facts in (3.27), and explain how they...Ch. 3.5 - Given (x1,y1), (x2,y2), (x3,y3), and (x4,y4), show...Ch. 3.5 - Plot the cure in Exercise 7.Ch. 3.5 - Prob. 2CPCh. 3.5 - Plot the letter from BĂ©zier curves: (a) W (b) B...Ch. 3.5 - Use the bezierdraw.m program of Section 3.5 to...Ch. 3.5 - Revise the draw program to accept an n8 matrix of...Ch. 3.5 - Using the template above and your favorite text...Ch. 3.5 - Prob. 4SACh. 3.5 - Although font information was a closely guarded...Ch. 3.5 - Prob. 6SA

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