Answered: Compute f(0.25) from the following data…

Compute f(0.25) from the following data using Backward Gregory – Newton Interpolation Formula (BGNIF at xo= -1 -1 0.5 0.55 0.6 0.65 0.7 f(x) -1 -1.375 -1.225625 -1.064 -0.880375 -0.677

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Suppose A is an area function of ƒ. What is the relationship betweenƒ and A?

A: The relationship between a function ƒ and its area function A depends on the specific context and…

Q: Q.4: Find the third order Lagrange interpolation polynomial using the following table to compute…

Q: f. Compute f(1.68) from the following data using Forward Newton-Gauss Interpolation Formula (FNGIF)…

A: To apply the Forward Newton-Gauss Interpolation formula, form the central difference table for the…

Q: For a given function f, determine the forward and backward difference approximation for f'(4)…

A: See the attachment

Q: The OLS residuals, eį, are defined as follows: a. Îi – Ôo – Ô₁ X₁. - b. yi-00-0₁ X₁. c. Yi - Yi. d.…

A: Ordinary least squares (OLS) regression is a statistical method of estimate the relationship between…

Q: Derive the relation between input and output power spectral densities

A: We'll use the idea of the transfer function to determine the relationship between the input and…

Q: 4175 2 4 35 3 ちち 2012ヶち 23,45 36

Q: Compute f(10.25) for a given set of data below using: 1. Lagrange Interpolating Polynomial 2.…

A: Solution : y=f(x) 1. Lagrange's Interpolation formula is,…

Q: At what point on the paraboloid y = x² + z² is the tangent plane parallel to the plane 3x + 2y + 3z…

A: Introduction: Let z=f(x, y) be the equation of a surface S in R3, and let P=(a, b, c) be a point on…

Q: 4. (S.15). For the given function f(x) = v2+r2, let ro = 0, r1 = 0.5, and r2 = 0.8. Construct a…

A: Given f(x) = 2+x2 Hence x f(x) 0 2+02 = 1.414 0.5 2+(0.5)2 = 1.5 0.8 2+(0.8)2 = 1.625…

Q: Show that the following function is normalized. Remember to square the function first. Show clear…

A: Given the function as

Q: Is it possible for φ(n) (the Euler's totient function) to be bigger than n?

A: The objective is to find the possibility (if any) for φ(n) (the Euler's totient function) to be…

Q: 3. Prove that Q(0) = 0.5 sing the definition of error function.

Q: determine the coefficient of determination,

A: The provided information is x y xy x2 y2 3 1.6 4.8 9 2.56 4 3.6 14.4 16 12.96 5 4.4 22 25…

Q: Construct the interpolating polynomial of degree four for the unequally spaced data by using, (a)…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Using the function f (x) = x3+ 0,4x2 + x, the following data set was created. Using this data set,…

A: x y=f(x) 0.2 0.224 0.3 0.363 0.4 0.528 0.5 0.725 0.6 0.960

Q: (3) Estimate the error involved in using the approximation cos x = 1- for |x| < 0.01

A: To estimate the error involved in using the approximation cosx≈1-x22 for x≤0.01 The Taylor series…

Q: 2. Give the table below: * 1.0 | 1.2 1.4 1.6 | 1.8 f(x) 0.23 0.34 0.45 0.58 0.63 Use Newton forward…

Q: A bullet is fired upward with its velocity against time given in the table below: Time t in seconds…

A: The given problem is to find the value of velocity of time t=16 from the given data using Lagrange…

Q: A researcher calculates a chi-square of 5.263 from a 2x4 chi-square test for independence where n =…

A: Cramer's V is the measure of association between the two nominal variable. It takes the value…

Q: Find the F.T of the following; f(t) = e-jwot %3D

A: Given: f(t)=e-jw0t we can write f(t)=e-jw0t.1 By using property y(t).e-jw0t→F.T2πδw+w0

Q: The rate of change r(t) (in thousands of articles per year) of the total number of research articles…

Q: Given the data: 2.1 2 1.4 2.7 3.4 3.2 y 12 8. 2 5. 10 17 Determine y at x= 2.5 using: a) Newton's…

Q: Calculate the value of f (8) using Newton's divided difference formula from the following table: 4 7…

A: solution: Find the value of f(8) Divided difference table Here…

Q: The data is known as in the table below: a). Determine the equation that represents the data, using…

Q: Which of the following is the estimate of r2 for the root of f (x) = -0.9x2+1.7x + 2.5 using…

A: Newton Rahoson method is an iterative method and use to find isolated roots of an equation f(x)=0.…

Q: 2) For the given datasets calculate the f(4), using. a) Newton's interpolating polynomials of order…

Q: 1. Using Newton's backward-differences, construct interpolating polynomials of degree one, two, and…

A: As you ask multiple questions and according to the rule I have to solve the first one only. Please…

Q: Compute f(10.25) for a given set of data below using: 1. Lagrange Interpolating Polynomial 2.…

Q: 3. Given the following data: 0.1 0.2 0.3 0.4 f(x) -0.29004986 -0.56079734 -0.81401972 -0.10100000…

Q: Compute f(1.75) from the following data using Lagrange Interpolation Formula -1 0.5 1.5 2.5 f(x) 15…

Q: . Use the f(x)= x³ - 2x² + x-3 Newton-Raphson iteration method to estimate the root of the folle…

Q: 1. Given the following data: 3 4. 6. f (x) 7 11 28 63 89 (a) Complete a Divided Difference Table for…

A: We are given the following data : x 0 2 3 4 6 f(x) 7 11 28 63 89 We have to compute: (a) A…

Q: Use the table below to find the indicated values: X 3 6 9 13 f-¹(1) = f-¹(12) = f-¹(7) = 14 f(x) 1 4…

A: By using the table below to find f-11, f-112, and f-17. x 3 6 9 13 14 fx 1 4 7 12 16

Q: Consider the function f(x) = x³ + 2x + 5. Estimate the root to eight significant digits using Newton…

A: The general form of an equation of degree 3 is given by ax3+bx2+cx+d=0, where a≠0. In this problem,…

Q: Consider the data given in the table: lo Find the least square approximation function in the form y…

Q: Interpolate the value of the f(2,1) using Lagrange's interpolation formula with the following set of…

Question

d. Compute f(0.25) from the following data using Backward Gregory – Newton Interpolation Formula (BGNIF) at x₀= -1

Compute f(0.25) from the following data using Backward Gregory – Newton Interpolation Formula (BGNIF)
at xo= -1
-1
0.5
0.55
0.6
0.65
0.7
f(x)
-1
-1.375
-1.225625
-1.064
-0.880375
-0.677

III.
BACKWARD GREGORY – NEWTON INTERPOLATION FORMULA (BGNIF)
r(r+ 1)
f(x) = fo + rAf.1 +
2!
r(r+1)(r+ 2)
A°f3 +
r(r+ 1)(r + 2)(r + 3)
Aªf-4 +
3!
4!
Where:
x- the value of x whose f(x) is required
X, - chosen from the table
x = X, + rh
х— Хо
r =
h

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

Step 2: Computation

Step 3: Computation

Step 4: Computation

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 19 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Interpolation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

the following Higher-Order LDE using the Exponential Shift method
Find f(7) using Newton- Gregory interpolation formula from the following table. 4 6. 8. f(x) 0 3 8 16
Given the following data, calculate by of the quadratic Newton's divided difference polynomial: f(x) = 0 f(x₁) = 0.65 f(x₂)=0.85 X₁ =1 X₁ = 2 X₂=3 Select one: a. -0.425 b.-0.225 c. None d.-0.625
Q.3: Determine the Lagrange interpolating polynomial by using second orderform for the given data and estimate f1) and fl1.7): 3.5 F(x) Good Luck 17 24
Employ Lagrange's interpolation method to find the value of f(x) using the following set of values when a = 1.7. Given that Lo(1.7) = 0.79, L1(1.7) = -0.63 and L2(1.7) = 0.54. 1.1 2.2 3.2 f(x) 3 4 7 3.63 O 3.74 1.11 8.67
Compute the Euler’s Totient function for the following numbers. Show all work.(i) φ(351) (ii) φ(784) (iii) φ(5681).
Q.4: Find the third order Lagrange interpolation polynomial using the following table to compute f(9.2) from the following data; x f(x) 9 8 2.07944 2.19722 9.5 2.25129 11 2.39789
c. Compute f(1.5) from the following data using Newton’s Divided Difference Formula (NDDF) at x0= 0 formula is given
The first divided difference f[xo, x1] for the following data is xo = 1, x1 = 10, f[æo] = 7, f[x1] = 23
Given the following difference table (evenly spaced data) for some function fod, use Newton Gregory interpoiating polynomial of degr estimate f(0.2) 0125 0.79151 001787 0.00794 025 0.77364 -0.00993 0.375 0.76371 Ca. 0.768715 b. 0.781983 Oc0.756917 d. 0.778193 e. 0.762863 E. 0.771861 9. 0.779835
1) Evaluate арх. C3 Itc 91 thoonem to