- 7-220.127.116.11: Compute the condition numbers of the following matrices relative to...
- 7-18.104.22.168: Compute the condition numbers of the following matrices relative to...
- 7-22.214.171.124: The following linear systems Ax = b have x as the actual solution a...
- 7-126.96.36.199: The following linear systems Ax = b have x as the actual solution a...
- 7-188.8.131.52: (i) First use Gaussian elimination and three-digit rounding arithme...
- 7-184.108.40.206: Repeat Exercise 5 using four-digit rounding arithmetic.
- 7-220.127.116.11: The linear system Ax = b, given by 1 2 1.0001 2 x1 x2 = 3 3.0001 ha...
- 7-18.104.22.168: The linear system Ax = b given by 1 2 1.00001 2 x1 x2 = 3 3.00001 h...
- 7-22.214.171.124: Show that if B is singular, then 1 K(A) ||A B|| ||A|| . [Hint: Ther...
- 7-126.96.36.199: Using Exercise 9, estimate the condition numbers for the following ...
- 7-188.8.131.52: The n n Hilbert matrix H(n) defined by H(n) i j = 1 i + j 1 , 1 i, ...
- 7-184.108.40.206: Use four-digit rounding arithmetic to compute the inverse H 1 of th...
Solutions for Chapter 7-4: Error Bounds and Iterative Refinement
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
An equation that relates variable quantities associated with phenomena being studied
Chord of a conic
A line segment with endpoints on the conic
Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian three-dimensional space
Differentiable at x = a
See Polar coordinates.
A set with no elements
The minimum, first quartile, median, third quartile, and maximum of a data set.
The domain of a function’s algebraic expression.
Initial side of an angle
Inverse cosine function
The function y = cos-1 x
Law of sines
sin A a = sin B b = sin C c
See Parametric equations.
Right-hand limit of ƒ at x a
The limit of ƒ as x approaches a from the right.
Slope-intercept form (of a line)
y = mx + b
Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series
A line graph in which time is measured on the horizontal axis.
See Weighted mean.
A point that lies on both the graph and the y-axis.
The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.