 3.2.1: Use Neville's method to obtain the approximations for Lagrange inte...
 3.2.2: Use Neville's method to obtain the approximations for Lagrange inte...
 3.2.3: Use Neville's method to approximate \/3 with the following function...
 3.2.4: Let Pji(x) be the interpolating polynomial for the data (0, 0), (0....
 3.2.5: Neville's method is used to approximate /(0.4), giving the followin...
 3.2.6: Neville's method is used to approximate /(0.5), giving the followin...
 3.2.7: Suppose X/ = 7, for 7 = 0, 1, 2, 3, and it is known that Po,i(x) = ...
 3.2.8: Suppose xy = 7, for 7 = 0, 1, 2, 3, and it is known that Po.1(x) = ...
 3.2.9: Neville's Algorithm is used to approximate /(0) using /(2), /(I), /...
 3.2.10: Neville's Algorithm is used to approximate /(G) using /(2), /(I), /...
 3.2.11: Construct a sequence of interpolating values y to /(I + VlO), where...
 3.2.12: Use iterated inverse interpolation to find an approximation to the ...
 3.2.13: Construct an algorithm that can be used for inverse interpolation.
Solutions for Chapter 3.2: Data Approximation and Neville's Method
Full solutions for Numerical Analysis  10th Edition
ISBN: 9781305253667
Solutions for Chapter 3.2: Data Approximation and Neville's Method
Get Full SolutionsSince 13 problems in chapter 3.2: Data Approximation and Neville's Method have been answered, more than 58081 students have viewed full stepbystep solutions from this chapter. Chapter 3.2: Data Approximation and Neville's Method includes 13 full stepbystep solutions. Numerical Analysis was written by and is associated to the ISBN: 9781305253667. This textbook survival guide was created for the textbook: Numerical Analysis, edition: 10. This expansive textbook survival guide covers the following chapters and their solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Column space C (A) =
space of all combinations of the columns of A.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.