- 7-18.104.22.168: Find the first two iterations of the Jacobi method for the followin...
- 7-22.214.171.124: Find the first two iterations of the Jacobi method for the followin...
- 7-126.96.36.199: Repeat Exercise 1 using the GaussSeidel method.
- 7-188.8.131.52: Repeat Exercise 2 using the GaussSeidel method.
- 7-184.108.40.206: Use the Jacobi method to solve the linear systems in Exercise 1, wi...
- 7-220.127.116.11: Use the Jacobi method to solve the linear systems in Exercise 2, wi...
- 7-18.104.22.168: Use the GaussSeidel method to solve the linear systems in Exercise ...
- 7-22.214.171.124: Use the GaussSeidel method to solve the linear systems in Exercise ...
- 7-126.96.36.199: Find the first two iterations of the SOR method with = 1.1 for the ...
- 7-188.8.131.52: Find the first two iterations of the SOR method with = 1.1 for the ...
- 7-184.108.40.206: Repeat Exercise 9 using = 1.3.
- 7-220.127.116.11: Repeat Exercise 10 using = 1.3.
- 7-18.104.22.168: Use the SOR method with = 1.2 to solve the linear systems in Exerci...
- 7-22.214.171.124: Use the SOR method with = 1.2 to solve the linear systems in Exerci...
- 7-126.96.36.199: Determine which matrices in Exercise 9 are tridiagonal and positive...
- 7-188.8.131.52: Determine which matrices in Exercise 10 are tridiagonal and positiv...
- 7-184.108.40.206: The linear system 2x1 x2 + x3 = 1, 2x1 + 2x2 + 2x3 = 4, x1 x2 + 2x3...
- 7-220.127.116.11: The linear system x1 + 2x2 2x3 = 7, x1 + x2 + x3 = 2, 2x1 + 2x2 + x...
- 7-18.104.22.168: The linear system x1 x3 = 0.2, 1 2 x1 + x2 1 4 x3 = 1.425, x1 1 2 x...
- 7-22.214.171.124: Repeat Exercise 19 using the Jacobi method.
- 7-126.96.36.199: a. Prove that x(k) xT k x(0) x and x(k) x T k 1 T x(1) x(0) , where...
- 7-188.8.131.52: Show that if A is strictly diagonally dominant, then ||Tj|| < 1.
- 7-184.108.40.206: Prove Theorem 7.24. [Hint: If 1,... ,n are eigenvalues of T, then d...
- 7-220.127.116.11: Suppose that an object can be at any one of n + 1 equally spaced po...
- 7-18.104.22.168: Use all the applicable methods in this section to solve the linear ...
- 7-22.214.171.124: Suppose that A is a positive definite. a. Show that we can write A ...
- 7-126.96.36.199: Extend the method of proof in Exercise 26 to the SOR method with 0 ...
- 7-188.8.131.52: The forces on the bridge truss described in the opening to this cha...
Solutions for Chapter 7-3: Iterative Techniques for Solving Linear Systems
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
See Inverse secant function.
Average rate of change of ƒ over [a, b]
The number ƒ(b) - ƒ(a) b - a, provided a ? b.
Complex numbers a + bi and a - bi
Conic section (or conic)
A curve obtained by intersecting a double-napped right circular cone with a plane
See Polar coordinates.
An identity involving a trigonometric function of 2u
Reciprocal of the period of a sinusoid.
Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.
Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0
Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth
Measure of spread
A measure that tells how widely distributed data are.
Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2
The process of fitting a polynomial of degree n to (n + 1) points.
See Viewing window.
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.
A variable that is affected by an explanatory variable.
An end behavior asymptote that is a slant line
Slope-intercept form (of a line)
y = mx + b
An identity involving a trigonometric function of u + v
Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>