Question: Let A be a 10 10 matrix with condition number 5 x 106. Suppose that the solution to a system Ax = b is

Let A be a 10 × 10 matrix with condition number 5 x 106. Suppose that the solution to a system Ax = b is computed using 15-digit decimal arithmetic and the relative residual ||r||∞/||b||∞, turns out to be approximately twice the machine epsilon. How many digits of accuracy would you expect to have in your computed solution? Explain.

Step by Step Solution

★★★★★

3.45 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The relative error in the ... 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 (936).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Compute the singular values and condition numbers of the 2 2, 3 3. and 4 4 Hilbert matrices. What is the smallest Hilbert matrix with condition number larger than 106?

Let A be a constant matrix. Suppose u(r) solves the initial value problem Prove that the solution to the initial value problem u(t0) = b. is equal to How are the solution trajectories related? u A u,...

(a) Show that the nonsingular system ax + by = p, ex -I- dy = q has the solution given by the determinantal ratios Where (b) Use Cramer's Rule (1.87) to solve the systems (i) x + 3y=13. 4x + 2y = 0...

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...

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...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

Show the parse trees for the two parses that the grammar assigns for sentence S1. S1: the train station bus rumbles [3 marks] (b) Give an algorithm for a bottom-up passive chart parser without...

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...

350 Specification and Verification II Explain how a register can be modelled either as a unit-delay, or with an explicit clock input. [4 marks] Describe the relationship between the two models. [4...

Carlton Co. and Palmer, Inc., are U.S.-based MNCs with subsidiaries in Mexico that distribute medical supplies (produced in the United States) to customers throughout Latin America. Both subsidiaries...

Aloha Banking Co. is studying ATM use in suburban Honolulu. A sample of 30 ATMs showed they were used the following number of times yesterday. 83 64 84 76 84 54 63 75 59 61 80 70 84 73 68 52 95 65 90...

BE5.13 (LO 3) Gomez Inc. will deposit $30,000 in a 6% fund at the end of each year for 8 years beginning December 31, 2025. What amount will be in the fund immediately after the last deposit?

Use a graph or table to determine the profit-maximizing level of output for a perfectly competitive firm in the short run and to determine all relevant costs, revenues, and profits at that level of...

If possible, use exact arithmetic or a rational format for calculations in balancing the following chemical reaction: PbN6 + CrMn2O8 ( Pb3O4 + Cr2O3 + MnO2 + NO using the vector equation approach...

The chemical reaction below can be used in some industrial processes, such as the production of arsene (AsH3). Use exact arithmetic or a rational format for calculations to balance this equation. MnS...

Find the general flow pattern of the network shown in the figure. Assuming that the flows are all nonnegative, what is the smallest possible value for x4? x3 80

find 3%, 7% and 12% Perpetuities. The Stack has just written and recorded the single greatest rock song ever made. The boys in the band believe that the royalties from this song will pay the band a...

Compute the present values of the following annuities first assuming that payments are made on the last day of the period and then assuming payments are made on the first day of the period: (Do not...

Alpha Electronics can purchase a needed service for $90 per unit. The same service can be provided by equipment that costs $110,000 and that will have a salvage value of zero at the end of 10 years....