Numerical analysis problem

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Numerical-Analysis

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Numerical analysis
Numerical Analysis

Consider the same five-data pair (x, y) and- Find the first and second derivatives exactly at x = c. (c is any x in your data!)- Obtain the three-point forward difference formula for the second order derivative with a remainder by using the Taylor series expansion. Calculate f¢¢(c) by using this formula for the data given.- Obtain the three-point backward difference formula for the second order derivative with a remainder by using the Taylor series expansion. Calculate f¢¢(c) by using this formula for the data given.- Obtain the three-point central difference formula for the second order derivative with a remainder by using the Taylor series expansion. Calculate f¢¢(c) by using this formula for the data given.You can choose any five data pair.
Numerical Analysis

Find numerical Jacobian for the following function of two variables at (N1, N1+2) using centered finite difference formulas. Choose appropriate step-size to minimize errors. F(x,y)=[ ?? ? + ?? 2 ln(?) ] ? 2 + ? −2 log2(x?)

numerical analysis

(−1,f(−1)=2),(0,f(0)=5)(−1,f(−1)=2),(0,f(0)=5)Select one:
this is numerical analysis. please do a and b 1. This problem is concerned with solving...

this is numerical analysis. please do a and b 1. This problem is concerned with solving the equation f(x) = 0 using Newton's method, assuming f is a smooth (Cº) function. (a) Write the iteration representing Newton's method for solving f(x) = 0 and briefly state under what conditions the iteration makes sense, (b) Write Newton's method for solving the equation x"" = 0, where m > 2 is an integer. Show that the convergence is linear, not quadratic, and...
I need proof of this numerical analysis theorem. This theorem is from Burden's Numerical analysis book....

I need proof of this numerical analysis theorem. This theorem is from Burden's Numerical analysis book. Please give me the detailed solution of this theorem. Theorem If {00, ... , ºn} is an orthogonal set of functions on an interval [a, b] with respect to the weight function w, then the least squares approximation to f on [a, b] with respect to w is 11 P(x) = a;°;(x), j=0 where, for each j = 0, 1, ... ,n, cb aj...

Numerical problem!

An unknown metal M reacts with S to form a compound with a formula M2S3. If 3.12g of m reacts with exactly 2.88g of sulfur, what are the names of metal M and compound M2S3?
NUMERICAL ANALYSIS ASSIGNMENT 1(MTH603)

Question:In this question, we are interested in finding x such that f(x) = 0, where f(x) = x − 𝑠in(x) − 0.01i. Use the fact that 𝑠in(x) ≈ x− x3/3! to estimate when f(x) = 0.ii. Apply two iteration of the Newton Raphson method to f(x) = 0. Use your estimate of the solution from part (i) as x^0. Do your calculation to at least four decimal places.iii. Which other method you have studied can converge to the solution faster...
numerical analysis question 3. For the matrix in problem 1, apply the Householder transformation to transform...

numerical analysis question 3. For the matrix in problem 1, apply the Householder transformation to transform A into an upper triangular matrix R. Express all the Householder transformation matrices p(1), p() explicitly. Based on the orthogonal matrices p(1), p(2) and the upper triangular matrix R, obtain the QR decomposition of the matrix A. A = | 1 4 il 2 3 2 -2 2 1

this is numerical analysis. please do a and b 2. Consider the non-standard interpolation problem: Given...

this is numerical analysis. please do a and b 2. Consider the non-standard interpolation problem: Given three numbers A, B, C and a fixed node & € R, find a quadratic polynomial 9(x) = 40 +213 + azra so that 9(-1) = A, d'(E) - B, 9(1) = C. (1) (a) Show that if & = 0, the problem is not well-posed, that is, there are numbers A, B, C for which the interpolation problem (1) has no solution (b)...