Question: If A is a nonsymmetric matrix and a numerically stable algorithm is used to compute the eigenvalues of Ax = b, then the relative error

If A is a nonsymmetric matrix and a numerically stable algorithm is used to compute the eigenvalues of Ax = b, then the relative error in the computed eigenvalues should always be small.
In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true.

Step by Step Solution

★★★★★

3.42 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The statement is false in general If the matrix is nonsymmetric then the eigenvalue ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

949-M-L-A-E (926).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

(a) Write a program for n Ã n matrices that prints every step. Apply it to the (nonsymmetric!) matrix (20 steps), starting from [1 1 1] T . (b) Experiment in (a) with shifting. Which shift do...

If A is a nonsingular matrix and a numerically stable algorithm is used to compute the solution to a system Ax = b, then the relative error in the computed solution will always be small. In the case...

If A is a symmetric matrix and a numerically stable algorithm is used to compute the eigenvalues of Ax = b, then the relative error in the computed eigenvalues should always be small. In the case of...

Math 400 Assignment #3 -- Numerical Integration and Differentiation 1. For the function g x e x 2 2 Due: 6am April 09, 2016 use the centered difference formula with h 101 , 102 , , 1020 to create a...

software projects failed. In the run-up to Y2K, most of the world's large companies claimed that fixing the Millennium Bug was a large project whose success was critical to their survival. One would...

(Q1) Let A be an nn matrix with real entries and distinct eigenvalues. There are a few ways to measure the condition of A. In general, the condition number is given by (A) = ||A|| ||A1 ||. It...

re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Define the contextual-equivalence relation ` M =ctx M0 : for pairs of PCF terms M, M0 , PCF types , and PCF type environments . [3 marks] (ii) For PCF terms M and N with respective typings ` M : and...

What are the required elements of the statute? In other words, for a contract for the sale of goods of $500 or more to be enforceable, what is required?

Lewis River Golf, Inc., grew and sold sod. It bought seed from defendant, O. M. Scott & Sons, under an express warranty. But the sod grown from the Scott seeds developed weeds, a breach of Scotts...

( : [ Regression Statistics ] , [ Multiple , 0 . 8 8 1 1 ] , [ R ]

Analyze how institutional characteristics and barriers to entry affect monopolistically competitive markets.

In Exercise 11 through 18, translate axes to identify the graph of each equation and write each equation in standard form? 1. x2 - y2 + 4x - 6y - 9 = 0 2. x2 - 4x + 4y + 4 = 0 3. 4x2 + 5y2 - 30y + 25...

In Exercise 19 through 24, rotate exes to identify the graph of each equation and write each equation in standard form? 1. xy = 1 2. x2 + y2 + 4xy = 9 3. 9x2 + 6y2 + 4xy - 5 = 0

In exercise 25 through 30, identify the graph and each equation and write each equation in standard form? 1. 5x2 + 5y2 - 6xy - 30(2x + 18(2y + 82 = 0 2. 6x2 + 9y2 - 4xy - 4(5x - 18(5 y = 5 3. 8x2 +...

Many fast food restaurant chains like McDonalds and others have some stores which are directly owned by the company (McDonalds) which hires a manager and staff to manage the restaurants, and some...

The following estimated regression equation is based on 30 observations. y^=17.4+3.8x12x2+7.6x3+2.8x4 The values of SST and SSR are 1,809 and 1,762 , respectively. a. Compute R2 (to 3 decimals). b....

Expected Return Standard Deviation Stock fund ( S ) 14% 34% Bond fund ( B ) 5% 28% The correlation between the fund returns is .0214. What is the expected return and standard deviation for the...