The task is to construct the natural cubic spline for the data provided in the tables below. You may use a matrix calculator to row reduce any matrices.**Table A:**| x | f(x) ||-----|-----------|| 0.8 | 0.22363362|| 1.0 | 0.65809197|**Table B:**| x | f(x) ||-----|-----------|| 0.1 | -0.29004996|| 0.2 | -0.56079734|| 0.3 | -0.81401972|The objective is to apply cubic spline interpolation to the given sets of discrete data points in tables A and B.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find LU factorization for the following matrix. 3 6 X = |-6 0 -16 8 -17
Use a graphing calculator to find the inverse of the matrix, if it exists.
Set up an augmentation matrix that would help to find the interpolating polynomial of degree at most 3 that passes through the points (0, 4), (1, 10), (–2,3), and (3, – 14). You DO NOT need to find the actual polynomial.
Please show every step. Please DO NOT skip a step. It is hard to follow or assume the step you took to solve the problem when steps are skipped.
Find the inverse of the following matrix. The constant a may be any real number. 0 -7 -5 a [ ] % -% a 5 -5 (B) (D) a 7 5 0 a -7 (E) (田)| ] (F) (G) -5
Find the inverse of the 45 x 45 matrix 1 23 0 0 1 2 0 1 ⠀⠀⠀ 000 000 ⠀⠀⠀ 44 45 43 44 42 43 1 0 ⠀ 2 1 To save a lot of typing, you do not need to input the entire matrix. Just enter the elements in its top-left corner, which are enough to establish the general pattern.

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Construct the natural cubic spline for the data in each of the following tables. You may use a matrix calculator to row reduce any matrices. A. x f(x) 0.8 0.22363362 1.0 0.65809197