Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Textbook Question
Chapter 3.3, Problem 2E
Find the upper bound for
on the intervals and Chebyshev nodes in Exercise 1.
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For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Year Month Units1 Nov 42,1611 Dec 44,1862 Jan 42,2272 Feb 45,4222 Mar 54,0752 Apr 50,9262 May 53,5722 Jun 54,9202 Jul 54,4492 Aug 56,0792 Sep 52,1772 Oct 50,0872 Nov 48,5132 Dec 49,2783 Jan 48,1343 Feb 54,8873 Mar 61,0643 Apr 53,3503 May 59,4673 Jun 59,3703 Jul 55,0883 Aug 59,3493 Sep 54,4723 Oct 53,164
Consider the table of values below.
x
y
2
64
3
48
4
36
5
27
Fill in the right side of the equation y= with an expression that makes each ordered pari (x,y) in the table a solution to the equation.
solving for x
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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