|
About 3307 results. 1294 free access solutions
| № |
Condition |
free/or 0.5$ |
| m53298 | Consider the 2×2 linear system (A+iB)(x +iy) = c+id with complex entries in component form:
(a11 + ib11)(x1 + iy1) + (a12 + ib12)(x2 + iy2) = c1 + id1,
(a11 + ib21)(x1 + iy1) + (a22 + ib22)(x2 + iy2) = c2 + id2.
a. Use the properties of complex numbers to convert this system to the equivalent 4×4 real linear
system
Ax − By = c,
Bx + Ay = d.
b. Solve the linear system
(1 − 2i)(x1 + iy1) + (3 + 2i)(x2 + iy2) = 5 + 2i,
(2 + i)(x1 + iy1) + (4 + 3i)(x2 + iy2) = 4 − i. |
buy |
| m53301 | Consider the boundary-value problem
Y" + y = 0, 0 ≤ x ≤ b, y(0) = 0, y(b) = B.
Find choices for b and B so that the boundary-value problem has |
buy |
| m53309 | Consider the differential equation
y = f (t, y), a ≤ t ≤ b, y(a) = α.
a. Show that
for some ξ , where ti < ξi < ti+2.
b. Part (a) suggests the difference method
wi+2 = 4wi+1 − 3wi − 2hf (ti ,wi), for i = 0, 1, . . . , N − 2.
Use this method to solve
y = 1 − y, 0≤ t ≤ 1, y(0) = 0,
With h = 0.1. Use the starting values w0 = 0 and w1 = y(t1) = 1 − e−0.1.
c. Repeat part (b) with h = 0.01 and w1 = 1 − e−0.01.
d. Analyze this method for consistency, stability, and convergence. |
buy |
| m53313 | Consider the follow sets of vectors. (i) Show that the set is linearly independent; (ii) use the Gram- Schmidt process to find a set of orthogonal vectors; (iii) determine a set of orthonormal vectors from the vectors in (ii).
a. v1 = (1, 1)t, v2 = (−2, 1)t
b. v1 = (1, 1, 0)t, v2 = (1, 0, 1)t, v3 = (0, 1, 1)t
c. v1 = (1, 1, 1, 1)t, v2 = (0, 2, 2, 2)t, v3 = (1, 0, 0, 1)t
d. v1 = (2, 2, 3, 2, 3)t, v2 = (2,−1, 0,−1, 0)t, v3 = (0, 0, 1, 0,−1)t, v4 = (1, 2,−1, 0,−1)t,
v5 = (0, 1, 0, −1, 0)t |
buy |
| m53314 | Consider the follow sets of vectors. (i) Show that the set is linearly independent; (ii) use the Gram-Schmidt process to find a set of orthogonal vectors; (iii) determine a set of orthonormal vectors from the vectors in (ii).
a. v1 = (2,−1)t, v2 = (1, 3)t
b. v1 = (2,−1, 1)t, v2 = (1, 0, 1)t, v3 = (0, 2, 0)t
c. v1 = (1, 1, 1, 1)t, v2 = (0, 1, 1, 1)t, v3 = (0, 0, 1, 0)t
d. v1 = (2, 2, 0, 2, 1)t, v2 = (−1, 2, 0,−1, 1)t, v3 = (0, 1, 0, 1, 0)t, v4 = (−1, 0, 0, 1, 1)t |
buy |
| m53318 | Consider the following Gaussian-elimination-Gauss-Jordan hybrid method for solving the system (6.4). First, apply the Gaussian-elimination technique to reduce the system to triangular form. Then use the nth equation to eliminate the coefficients of xn in each of the first n − 1 rows. After this is completed use the (n − 1)st equation to eliminate the coefficients of xn−1 in the first n − 2 rows, etc. The system will eventually appear as the reduced system in Exercise 12.
a. Show that this method requires
n3/3 + 3/2 n2 - 5/6 n multiplications/divisions
and
n3/3 + n2/2 - 5/6 n additions/subtractions.
b. Make a table comparing the required operations for the Gaussian elimination, Gauss-Jordan, and hybrid methods, for n = 3, 10, 50, 100. |
buy |
| m53338 | Consider the following matrices. Find the permutation matrix P so that PA can be factored into the product LU, where L is lower triangular with 1s on its diagonal and U is upper triangular for these matrices.
a.
b.
c.
d. |
buy |
| m53339 | Consider the following matrices. Find the permutation matrix P so that PA can be factored into the product LU, where L is lower triangular with 1s on its diagonal and U is upper triangular for these matrices.
a.
b.
c.
d. |
buy |
| m53352 | Consider the following table of data:
a. Use all the appropriate formulas given in this section to approximate f (0.4) and f (0.4).
b. Use all the appropriate formulas given in this section to approximate f (0.6) and f (0.6). |
buy |
| m53353 | Consider the following table of data:
a. Use Eq. (4.7) to approximate f (0.2).
b. Use Eq. (4.7) to approximate f (1.0).
c. Use Eq. (4.6) to approximate f (0.6). |
buy |
| m53355 | Consider the four 3 × 3 linear systems having the same coefficient matrix:
2x1 − 3x2 + x3 = 2, 2x1 − 3x2 + x3 = 6,
x1 + x2 − x3 = −1, x1 + x2 − x3 = 4,
−x1 + x2 − 3x3 = 0; −x1 + x2 − 3x3 = 5;
2x1 − 3x2 + x3 = 0, 2x1 − 3x2 + x3 = −1,
x1 + x2 − x3 = 1, x1 + x2 − x3 = 0,
−x1 + x2 − 3x3 = −3; −x1 + x2 − 3x3 = 0.
a. Solve the linear systems by applying Gaussian elimination to the augmented matrix
b. Solve the linear systems by finding and multiplying by the inverse of
c. Which method requires more operations? |
buy |
| m53358 | Consider the function
e(h) = ε/h+ h2/6 M,
Where M is a bound for the third derivative of a function Show that e(h) has a minimum at 3√(3ε/M). |
buy |
| m53445 | Construct a natural cubic spline to approximate f (x) = cos πx by using the values given by f (x) at x = 0, 0.25, 0.5, 0.75, and 1.0. Integrate the spline over [0, 1], and compare the result to
0. Use the derivatives of the spline to approximate f (0.5) and f (0.5). Compare these approximations to the actual values. |
buy |
| m53446 | Construct a natural cubic spline to approximate f (x) = e−x by using the values given by f (x) at x = 0, 0.25, 0.75, and 1.0. Integrate the spline over [0, 1], and compare the result to
Use the derivatives of the spline to approximate f (0.5) and f (0.5). Compare the approximations to the actual values. |
buy |
| m53451 | Construct a sequence of interpolating values yn to f (1 + √10), where f (x) = (1 + x2)−1 for −5 ≤ x ≤ 5, as follows: For each n = 1, 2, . . . , 10, let h = 10/n and yn = Pn(1+√10), where Pn(x) is the interpolating polynomial for f (x) at the nodes x0(n) , x1(n) , . . . , xn(n) and xj(n) = −5 + jh, for each
j = 0, 1, 2, . . . , n. Does the sequence {yn} appear to converge to f (1 +√10)? |
buy |
| m53454 | Construct an AdamsVariable Step-Size Predictor-Corrector Algorithm based on the Adams-Bashforth five-step method and the Adams-Moulton four-step method. Repeat Exercise 3 using this newmethod.
In Exercise 3 |
buy |
| m53455 | Construct an algorithm for the complete pivoting procedure discussed in the text. |
buy |
| m53456 | Construct an algorithm similar to Algorithm 12.1, except use the SOR method with optimal ω instead of the Gauss-Seidel method for solving the linear system. |
buy |
| m53457 | Construct an algorithm that can be used for inverse interpolation. |
buy |
| m53458 | Construct an algorithm that has as input an integer n ≥ 1, numbers x0, x1, . . . , xn, and a number x and that produces as output the product (x − x0)(x − x1) · · · (x − xn). |
buy |
|