Numerical Methods
4th Edition
ISBN: 9780495114765
Author: J. Douglas Faires, BURDEN
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 3.3, Problem 5E
a.
To determine
Calculate the polynomial using Newton’s forward difference interpolation method at most 4.
b.
To determine
Calculate the polynomial using Newton’s difference interpolation method at most 1, 2 and 3.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Find E(X) and if students pay $500 per course plus a $100 per-semester registration fee., What is the average amount of money the university can expect to make from a student each a semester?
Use the data in the table to approximate the acceleration at time t=1.4 hours
Use the following data and the Newton forward-difference formula to approximate f(0.05).
x= 0.0, 0.2, 0.4, 0.6, 0.8
f(x) = 1.0, 1.22140, 1.49182, 1.82212, 2.22554
Then use Newton backward divided-difference formula to approximate f(0.65) for the same values.
Chapter 3 Solutions
Numerical Methods
Ch. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Use appropriate Lagrange interpolating polynomials...Ch. 3.2 - Use Nevilles method to obtain the approximations...Ch. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Use the Lagrange interpolating polynomial of...Ch. 3.2 - Prob. 9ECh. 3.2 - Prob. 10E
Ch. 3.2 - Prob. 11ECh. 3.2 - Nevilles method is used to approximate f(0.5),...Ch. 3.2 - Prob. 13ECh. 3.2 - Suppose xj=j for j=0,1,2,3 and it is known that...Ch. 3.2 - Nevilles method is used to approximate f(0) using...Ch. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - A fourth-degree polynomial P(x) satisfies...Ch. 3.3 - Prob. 10ECh. 3.3 - The Newton forward divided-difference formula is...Ch. 3.3 - For a function f, the Newtons interpolatory...Ch. 3.3 - Prob. 13ECh. 3.4 - Use Hermite interpolation to construct an...Ch. 3.4 - Prob. 2ECh. 3.4 - Use the following values and five-digit rounding...Ch. 3.4 - Let f(x)=3xexe2x Approximate f(1.03) by the...Ch. 3.4 - Prob. 5ECh. 3.4 - The following table lists data for the function...Ch. 3.4 - A car traveling along a straight road is clocked...Ch. 3.4 - Prob. 8ECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - The data in Exercise 3 were generated using the...Ch. 3.5 - Construct the clamped cubic spline using the data...Ch. 3.5 - Repeat Exercise 4 using the clamped cubic splines...Ch. 3.5 - Prob. 7ECh. 3.5 - Construct a natural cubic spline to approximate...Ch. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - A clamped cubic spline s for a function f is...Ch. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Suppose that f(x) is a polynomial of degree 3....Ch. 3.5 - Suppose the data xi,fxi)i=1n lie on a straight...Ch. 3.5 - The data in the following table give the...Ch. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - It is suspected that the high amounts of tannin in...Ch. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Construct and graph the cubic BĂ©zier polynomials...Ch. 3.6 - Prob. 4E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.arrow_forwardRepeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.arrow_forwardThe formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
03a: Numerical Differentiation Review; Author: Jaisohn Kim;https://www.youtube.com/watch?v=IMYsqbV4CEg;License: Standard YouTube License, CC-BY