- 9-18.104.22.168: Find the first three iterations obtained by the Power method applie...
- 9-22.214.171.124: Find the first three iterations obtained by the Power method applie...
- 9-126.96.36.199: Repeat Exercise 1 using the Inverse Power method.
- 9-188.8.131.52: Repeat Exercise 2 using the Inverse Power method.
- 9-184.108.40.206: Repeat Exercise 2 using the Inverse Power method.
- 9-220.127.116.11: Find the first three iterations obtained by the Symmetric Power met...
- 9-18.104.22.168: Use the Power method to approximate the most dominant eigenvalue of...
- 9-22.214.171.124: Use the Power method to approximate the most dominant eigenvalue of...
- 9-126.96.36.199: Use the Inverse Power method to approximate an eigenvalue of the ma...
- 9-188.8.131.52: Use the Inverse Power method to approximate an eigenvalue of the ma...
- 9-184.108.40.206: Use the Symmetric Power method to approximate the most dominant eig...
- 9-220.127.116.11: Use the Symmetric Power method to approximate the most dominant eig...
- 9-18.104.22.168: Use Wielandt deflation and the results of Exercise 7 to approximate...
- 9-22.214.171.124: Use Wielandt deflation and the results of Exercise 8 to approximate...
- 9-126.96.36.199: Repeat Exercise 7 using Aitkens 2 technique and the Power method fo...
- 9-188.8.131.52: Repeat Exercise 8 using Aitkens 2 technique and the Power method fo...
- 9-184.108.40.206: Hotelling Deflation Assume that the largest eigenvalue 1 in magnitu...
- 9-220.127.116.11: Annihilation Technique Suppose the n n matrix A has eigenvalues 1,....
- 9-18.104.22.168: Following along the line of Exercise 11 in Section 6.3 and Exercise...
- 9-22.214.171.124: Show that the ith row of B = A 1v(1) xt is zero, where 1 is the lar...
- 9-126.96.36.199: The (m 1) (m 1) tridiagonal matrix A = 1 + 2 0 0 1 + 2 0 0 0 0 1 + ...
- 9-188.8.131.52: The eigenvalues of the matrix A in Exercise 21 are i = 1 + 4 sin i ...
- 9-184.108.40.206: The (m 1) (m 1) matrices A and B given by A = 1 + 2 0 0 2 1 + 2 0 0...
- 9-220.127.116.11: A linear dynamical system can be represented by the equations dx dt...
Solutions for Chapter 9-2: The Power Method
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
Average rate of change of ƒ over [a, b]
The number ƒ(b) - ƒ(a) b - a, provided a ? b.
The process of utilizing general information to prove a specific hypothesis
An event whose probability depends on another event already occurring
Difference of complex numbers
(a + bi) - (c + di) = (a - c) + (b - d)i
An angle formed by two intersecting planes,
A method of solving a system of n linear equations in n unknowns.
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a
Mean (of a set of data)
The sum of all the data divided by the total number of items
The various possible results of an experiment.
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).
Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.
Polynomial in x
An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.
Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.
Two points that are symmetric with respect to a lineor a point.
Sample standard deviation
The standard deviation computed using only a sample of the entire population.
The function y = sec x.
Angle measure equal to 1/60 of a minute.
Standard representation of a vector
A representative arrow with its initial point at the origin
A number that measures a quantitative variable for a sample from a population.