#5: A QR-decomposition of A is given. Use it to find the least squares solution of Ax = b.13V8585V85V85[]A =;b =6.V85V85V85Enter the components of the least squares solution x [x y]' into the answer box below (in order), separated witha comma.

We are given the QR-decomposition of the matrix A And using that we have to find the least square…

Answered: A QR-decomposition of A is given. Use…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

See similar textbooks

Similar questions

You are given 6 data points (xi; yi) below, where i = 1,..., 6 that are observed from a model: y = a3x3 + a2x2 + a1x + a0 + n, where n is a zero-mean Gaussian noise. Estimate the coefficients: a0,...,a3 by setting up a linear system of equations, and solving it using least squares. (x1,y1) = (-3, -171.17478734011377) (x2, y2) = (-1.5, -26.283603386675573) (x3, y3) = (0, 10.342025892375206) (x4, y4) = (2, 34.71284310507833 (x5, y5) = (5.5, 733.5702844691194) (x6, y6) = (7, 1546.4530015969324)
Starting from the linearly independent functions yn(x) = xn where n = 0, 1, · · · , use Gram–Schmidt orthogonalisation to construct the first three orthonormal functions over the range −1 < x < 1, assuming a weight function of unity, and verify that they are mutually orthogonal.
Transform the nth-order equationy(n) = a0y + a1y' +· · ·+an−1y(n−1)into a system of first-order equations by settingy1 = y and yj = y;j−1 for j = 2, . . . , n. Determinethe characteristic polynomial of the coefficientmatrix of this system.
(a) find the least squares approximation g(x) = a0 + a1x + a2x2 of the function f, and (b) use a graphing utility to graph f and g in the same viewing window. f (x) = cos x, −π/2 ≤ x ≤ π/2
Prove that if x0 is a critical point of f and Hf (x0) is positive de nida, then f has a local minimum at x0. Where Hf is the Hessian matrix
Question 1. Determine the LU decomposition with pivoting by hand. 3x1 - 2x2 +x3 = -10 2x1 + 6x2 -4x3 = 44 -x1 - 2x2 + 5x3 = -26 Question 2.Use MATLAB for a,b,c and d. And show your solution and coding steps by MATLAB. a) Check your results by validating that [L][U] = [A] b)Solve the system of equations by using the backslash approach. c) Use the inverse to determine the solution. d)Determine the matrix inverse. Check your results by verifying that [A] [A]-1 = [I]
For the matrix A and the vector z_0 given below apply the Power Methodthree times to find approximate values for the dominant eigenvalue and thecorresponding eigenvector. So stuck!!!!!!!!!
Consider the ODE eigenvalue problem: ((1-x2)1/2φ')' + λ(1-x2)-1/2φ = 0 posed for -1 < x < 1 and subject to the boundary condidiont |φ(-1)| < ∞ and |φ(1)| < ∞. If you find it helpful you, you may assume |φ'(-1)| < ∞ and |φ'(1)| < ∞. a) Show that this is a Sturm-Liouville eigenvalue problem, i.e, verify that it has the correct form and identify the coefficients p, q, and σ. Is the problem regular? Why or why not? b) Show that λ > 0 for each eigenvalue λ.
Using least-squares regression, find a straight line that best fits the data in Table 1 below. xi yi 0.2 8.2 0.4 8.4 0.6 8.5 0.8 8.6 1.0 8.8 1.2 8.7 b. Using table 1 above, find the second-degree Lagrange interpolating polynomial that goes through the first three data points, and use it to find the interpolated value at xi = 0.48.
Let A be a 2 × 2 matrix with Schur decompositionUTUH and suppose that t12 ≠= 0. Show that the eigenvalues of A are λ1 = t11 and λ2 = t22.
Evaluate (x1(t) + z1(t) / y1(t)) for the solution [x1(t), y1(t), z1(t)] that corresponds to the eigenvalue lambda = 0 of the following system...
1. Find the linearization of x3 − x at a = 2.

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS

A QR-decomposition of A is given. Use it to find the least squares solution of Ax = b. 13 85 V85 V85 V85 [] A = ;b = 7 1 V85 V85 V85 Enter the components of the least squares solution x [x y] into the answer box below (in order), separated with a comma.