Explain how you can use QR factorization to solve the following problem Find x1 and x2...

Explain how you can use QR factorization to solve the following problem

Find x1 and x2 that minimize ||Ax1 − b1||^2 + ||Ax2 − b2||^2. The problem data are the m× n matrix A,
and the m-vectors b1 and b2. The matrix A has linearly independent columns.

Expert Solution

Colby Messinger answered 2 years ago

Explain how you can solve the following problems using the QR factorization. (a) Find the vector...

Explain how you can solve the following problems using the QR factorization. (a) Find the vector x that minimizes ||Ax − b1||^2 + ||Ax − b2||^2 . The problem data are the m × n matrix A and two m-vectors b1 and b2. The matrix A has linearly independent columns. If you know several methods, give the most efficient one. (b) Find x1 and x2 that minimize ||Ax1 − b1||^2 + ||Ax2 − b2||^2 . The problem data are the...

Use any method you like to determine a reduced QR factorization A = QR and a...

Use any method you like to determine a reduced QR factorization A = QR and a full QR factorization A= QR

Consider the following constrained maximization problem. maxln(x1,x2) s.t.z-x1-x2=0 Solve for x1and x2using substation method Solve for...

Consider the following constrained maximization problem. maxln(x1,x2) s.t.z-x1-x2=0 Solve for x1and x2using substation method Solve for x1and x2using Lagrange’s method

use newton raphson method to solve the following system of nonlinear equations x1^2+x2^2=50 ; x1*x2=25 stop...

use newton raphson method to solve the following system of nonlinear equations x1^2+x2^2=50 ; x1*x2=25 stop after three iterations. initial guess : (x1,x2) = (2,1)

Solve the following linear programming problem by solver. Maximize Z = 7 x1 + 5 x2...

Solve the following linear programming problem by solver. Maximize Z = 7 x1 + 5 x2 + 5 x3 subject to x1 + x2 + x3 <= 25 2 x1 + x2 + x3 <= 40 x1 + x2 <= 25 x3 <= 6 x1, x2, x3 >= 0 (non-negativity conditions)

use the two-phase method and big.M method to solve the LPP: min z=x1-2x2 st: x1+x2>=2 -x1+x2>=1...

use the two-phase method and big.M method to solve the LPP: min z=x1-2x2 st: x1+x2>=2 -x1+x2>=1 x2<=3 x1,x2>=0 (two method!)

Using Matlab 1. Solve the following equations set f1 (x1,x2) = sin (sin (x1)) +x2 f2...

Using Matlab 1. Solve the following equations set f1 (x1,x2) = sin (sin (x1)) +x2 f2 (x1,x2) = x1+ e^(x2) a) Can this equation set be solved by the fixed - point method with the following expressions? And why? Show your analysis with a 2D graph. g1 (x1,x2) = -e^(x2) g2 (x1,x2) = -sin⁡(x1) b) Use Newton Raphson Method with initial values x1 = -2, x2 = 1.5. (8 significant figures. Please submit the code and results.)

Solve the following LP problem using graphical solution method. MAX: 5 X1 + 3 X2 Subject...

Solve the following LP problem using graphical solution method. MAX: 5 X1 + 3 X2 Subject to: 2 X1 − 1 X2 ≤ 2 6 X1 + 6 X2 ≥ 12 1 X1 + 3 X2 ≤ 5 X1, X2 ≥ 0

19. Suppose you find that MU1( x1,x2)=2x2 and MU2( x1,x2)=2x1. What is the rate at which...

19. Suppose you find that MU1( x1,x2)=2x2 and MU2( x1,x2)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional—marginal—unit of good 1.) 20. Suppose you find that the expressions of the marginal utilities for a consumer are given by MU1( x1,x2)=1 and MU2( x1,x 2)=3. Then...

Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0. elsewhere (a) Find the...

Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0. elsewhere (a) Find the conditional densities (pdf) of X1|X2 = x2 and X2|X1 = x1. (b) Find the conditional expectation and variance of X1|X2 = x2 and X2|X1 = x1. (c) Compare the probabilities P(0 < X1 < 1/2|X2 = 3/4) and P(0 < X1 < 1/2). (d) Suppose that Y = E(X2|X1). Verify that E(Y ) = E(X2), and that var(Y ) ≤ var(X2).

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