(1) Let ž. be an approximate solution. Calculate the relative forward error, relative back- ward error, and error magnification factor for this approximate solution (use infinity norm). (ii) Find the condition number of matrix A (using infinity norm). (iii) For a system of linear equations Až = b, what is the possible consequence of an extremely large condition number of A?

(1) Let ž. be an approximate solution. Calculate the relative forward error, relative back- ward error, and error magnification factor for this approximate solution (use infinity norm). (ii) Find the condition number of matrix A (using infinity norm). (iii) For a system of linear equations Až = b, what is the possible consequence of an extremely large condition number of A?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Answer the question
State the general form of a particular solution to y" + 3y' – y = 3te-24. (Do not solve for the constants associated with the particular solution.)
(b) For each augmented matrix determine how many solution the associated system of linear equations has: 1200 0120 0000 (i) 0 1 20 (ii) 0012 (iii) 1200 0012 0001 0120
Find the rank and the nullity of the matrix rank (A) = nullity (A) = = rank(A) + nullity (A) = choose > A = -1 -2 -1 -2 -1 3 0 -1 -2 -1 2-5 TT 3 -8
2. Suppose that the rref of an augmented matrix of a linear system results as 1 0 1 13 0 1 0 21 000 00 (a) What are the leading variables? (b) What are the free variables? (c) What is the corresponding system of equations in terms of the free variables. (d) Write the solutions in vector form.
By using the method of least squares, find the best line through the points: (−2,−1), (2,1), (0,–3). Step 1. The general equation of a line is c + ₁ = y. Plugging the data points into this formula gives a matrix equation Ac = y. Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation ATA ĉ = A¹y ATA= ATy = Step 3. Solving the normal equation gives the answer Ĉ= which corresponds to the formula y = Analysis. Compute the predicted y values: y ŷ = Compute the error vector: e=y-ŷ. = Aĉ. Compute the total error: SSE = e² + e² + ez. SSE =
solve both (a) and (b)
Please teach how to solve not just solve (concepts) .) Consider the linear function from R³ → R³ defined by the matrix: ^= 1) -5 -6 7 A 8 -9 0 -3 В Calculate tr(A). (Show that the set of column vectors of the following matrix, are linearly independent: -5 -6 7 -9 0 A = 8 -3 В α. You should substitute the values of a, ẞ that you calculated in part (b). Show all necessary steps. Could the matrix A above be the Hessian matrix of a R³ → R function? Give a one or two sentence explanation. (, Once again, consider the matrix: -5 -6 7 -9 0 B α A = 8 -3
Suppose (). (C) are solutions to a 2-dimensional homogeneous linear system. (a) Find the coefficient matrix of this system. (b) Find the general solution of this system.
True or False. Rank (A)+Nullity(A)=m for any matrix A of size nxm.