Numerical Analysis Burden Solutions Manual 9th Edition Download
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Chapter 1
Mathematical Preliminaries And Error Analysis
1-1 | Review of Calculus | Exercises Set | p.11 |
Discussion Question | p.14 | ||
1-2 | Round-off-Errors and Computer Arithmetic | Exercises Set | p.25 |
Discussion Question | p.29 | ||
1-3 | Algorithms and Convergence | Exercises Set | p.35 |
Discussion Question | p.38 | ||
1-4 | Numerical Software | Discussion Question | p.44 |
Chapter 2
Solutions Of Equations In One Variable
2-1 | The Bisection Method | Exercises Set | p.53 |
Discussion Question | p.54 | ||
2-2 | Fixed-Point Iteration | Exercises Set | p.63 |
Discussion Question | p.66 | ||
2-3 | Newton's Method and Its Extensions | Exercises Set | p.74 |
Discussion Question | p.78 | ||
2-4 | Error Analysis for Iterative Methods | Exercises Set | p.84 |
Discussion Question | p.85 | ||
2-5 | Accelerating Convergence | Exercises Set | p.89 |
Discussion Question | p.91 | ||
2-6 | Zeros of Polynomials and Muller's Method | Exercises Set | p.99 |
Discussion Question | p.100 | ||
2-7 | Numerical Software and Chapter Review | Discussion Question | p.101 |
Chapter 3
Interpolation And Polynomial Approximation
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3-1 | Interpolation and the Lagrange Polynomial | Exercises Set | p.112 |
Discussion Question | p.115 | ||
3-2 | Data Approximation and Neville's Method | Exercises Set | p.120 |
Discussion Question | p.122 | ||
3-3 | Divided Differences | Exercises Set | p.130 |
Discussion Question | p.133 | ||
3-4 | Hermite Interpolation | Exercises Set | p.139 |
Discussion Question | p.141 | ||
3-5 | Cubic Spline Interpolation | Exercises Set | p.158 |
Discussion Question | p.162 | ||
3-6 | Parametric Curves | Exercises Set | p.167 |
Discussion Question | p.168 | ||
3-7 | Numerical Software and Chapter Review | Discussion Question | p.169 |
Chapter 4
Numerical Differentiation And Integration
Numerical Analysis Burden Solutions Manual 9th Edition Download Full
4-1 | Numerical Differentiation | Exercises Set | p.180 |
Discussion Question | p.183 | ||
4-2 | Richardson's Extrapolation | Exercises Set | p.189 |
Discussion Question | p.191 | ||
4-3 | Elements of Numerical Integration | Exercises Set | p.200 |
Discussion Question | p.201 | ||
4-4 | Composite Numerical Integration | Exercises Set | p.208 |
Discussion Question | p.211 | ||
4-5 | Romberg Integration | Exercises Set | p.217 |
Discussion Question | p.219 | ||
4-6 | Adaptive Quadrature Methods | Exercises Set | p.226 |
Discussion Question | p.228 | ||
4-7 | Gaussian Quadrature | Exercises Set | p.234 |
Discussion Question | p.235 | ||
4-8 | Multiple Integrals | Exercises Set | p.248 |
Discussion Question | p.250 | ||
4-9 | Improper Integrals | Exercises Set | p.255 |
Discussion Question | p.256 | ||
4-10 | Numerical Software and Chapter Review | Discussion Question | p.257 |
Chapter 5
Initial-Value Problems For Ordinary Differential Equations
5-1 | The Elementary Theory of Initial-Value Problems | Exercises Set | p.264 |
Discussion Question | p.265 | ||
5-2 | Euler's Method | Exercises Set | p.272 |
Discussion Question | p.275 | ||
5-3 | Higher-Order Taylor Methods | Exercises Set | p.280 |
Discussion Question | p.282 | ||
5-4 | Runge-Kutta Methods | Exercises Set | p.291 |
Discussion Question | p.293 | ||
5-5 | Error Control and the Runge-Kutta-Fehlberg Method | Exercises Set | p.300 |
Discussion Question | p.302 | ||
5-6 | Multistep Methods | Exercises Set | p.314 |
Discussion Question | p.316 | ||
5-7 | Variable Step-Size Multistep Methods | Exercises Set | p.321 |
Discussion Question | p.322 | ||
5-8 | Extrapolation Methods | Exercises Set | p.329 |
Discussion Question | p.330 | ||
5-9 | Higher-Order Equations and Systems of Differential Equations | Exercises Set | p.337 |
Discussion Question | p.339 | ||
5-10 | Stability | Exercises Set | p.348 |
Discussion Question | p.349 | ||
5-11 | Stiff Differential Equations | Exercises Set | p.355 |
Discussion Question (5-11) | p.356 | ||
5-12 | Numerical Software | Discussion Question (5-12) | p.357 |
Chapter 6
Direct Methods For Solving Linear Systems
6-1 | Linear Systems of Equations | Exercises Set | p.371 |
Discussion Question | p.375 | ||
6-2 | Pivoting Strategies | Exercises Set | p.383 |
Discussion Question | p.385 | ||
6-3 | Linear Algebra and Matrix Inversion | Exercises Set | p.394 |
Discussion Question | p.400 | ||
6-4 | The Determinant of a Matrix | Exercises Set | p.403 |
Discussion Question | p.406 | ||
6-5 | Matrix Factorization | Exercises Set | p.413 |
Discussion Question | p.416 | ||
6-6 | Special Types of Matrices | Exercises Set | p.429 |
Discussion Question (6-6) | p.433 | ||
6-7 | Numerical Software | Discussion Question (6-7) | p.433 |
Chapter 7
Iterative Techniques In Matrix Algebra
7-1 | Norms of Vectors and Matrices | Exercises Set | p.447 |
Discussion Question | p.449 | ||
7-2 | Eigenvalues and Eigenvectors | Exercises Set | p.454 |
Discussion Question | p.456 | ||
7-3 | The Jacobian and Gauss-Siedal Iterative Techniques | Exercises Set | p.465 |
Discussion Question | p.468 | ||
7-4 | Relaxation Techniques for Solving Linear Systems | Exercises Set | p.473 |
Discussion Question | p.476 | ||
7-5 | Error Bounds and Iterative Refinement | Exercises Set | p.484 |
Discussion Question | p.486 | ||
7-6 | The Conjugate Gradient Method | Exercises Set | p.499 |
7-7 | Numerical Software | Discussion Question (7-7) | p.504 |
7-6 | The Conjugate Gradient Method | Discussion Question (7-6) | p.504 |
Chapter 8
Approximation Theory
8-1 | Discrete Least Squares Approximation | Exercises Set | p.514 |
Discussion Question | p.517 | ||
8-2 | Orthogonal Polynomials and Least Squares Approximation | Exercises Set | p.524 |
Discussion Question | p.525 | ||
8-3 | Chebyshev Polynomials and Economization of Power Series | Exercises Set | p.534 |
Discussion Question | p.535 | ||
8-4 | Rational Function Approximation | Exercises Set | p.544 |
Discussion Question | p.545 | ||
8-5 | Trigonometric Polynomial Approximation | Exercises Set | p.553 |
Discussion Question | p.555 | ||
8-6 | Fast Fourier Transforms | Exercises Set | p.565 |
8-7 | Numerical Software | Discussion Question (8-7) | p.567 |
8-6 | Fast Fourier Transforms | Discussion Question (8-6) | p.567 |
Chapter 9
Approximating Eigenvalues
9-1 | Linear Algebra and Eigenvalues | Exercises Set | p.576 |
Discussion Question | p.578 | ||
9-2 | Orthogonal Matrices and Similarity Transformations | Exercises Set | p.582 |
Discussion Question | p.585 | ||
9-3 | The Power Method | Exercises Set | p.599 |
Discussion Question | p.602 | ||
9-4 | Householder's Method | Exercises Set | p.609 |
Discussion Question | p.610 | ||
9-5 | The QR Algorithm | Exercises Set | p.621 |
Discussion Question | p.624 | ||
9-6 | Singular Value Decomposition | Exercises Set | p.636 |
Discussion Question (9-6) | p.637 | ||
9-7 | Numerical Software | Discussion Question (9-7) | p.638 |
Chapter 10
Numerical Solutions Of Nonlinear Systems Of Equations
10-1 | Fixed Points for Functions of Several Variables | Exercises Set | p.648 |
Discussion Question | p.651 | ||
10-2 | Newton's Method | Exercises Set | p.655 |
Discussion Question | p.658 | ||
10-3 | Quasi-Newton Methods | Exercises Set | p.664 |
Discussion Question | p.666 | ||
10-4 | Steepest Descent Technologies | Exercises Set | p.672 |
Discussion Question | p.673 | ||
10-5 | Homotopy and Continuation Methods | Exercises Set | p.680 |
10-6 | Numerical Software | Discussion Question (10-6) | p.682 |
10-5 | Homotopy and Continuation Methods | Discussion Question (10-5) | p.682 |
Chapter 11
Boundary-Value Problems For Ordinary Differential Equations
11-1 | The Linear Shooting Method | Exercises Set | p.692 |
Discussion Question | p.693 | ||
11-2 | The Shooting Method for Nonlinear Problems | Exercises Set | p.699 |
Discussion Question | p.699 | ||
11-3 | Finite-Difference Methods for Linear Problems | Exercises Set | p.704 |
Discussion Question | p.706 | ||
11-4 | Finite-Difference Methods for Nonlinear Problems | Exercises Set | p.711 |
Discussion Question | p.712 | ||
11-5 | The Rayleigh-Ritz Method | Exercises Set | p.726 |
11-6 | Numerical Software | Discussion Question (11-6) | p.728 |
11-5 | The Rayleigh-Ritz Method | Discussion Question (11-5) | p.728 |
Chapter 12
Numerical Solutions To Partial Differential Equations
12-1 | Elliptic Partial Differential Equations | Exercises Set | p.741 |
Discussion Question | p.743 | ||
12-2 | Parabolic Partial Differential Equations | Exercises Set | p.754 |
Discussion Question | p.757 | ||
12-3 | Hyperbolic Partial Differential Equations | Exercises Set | p.763 |
Discussion Question | p.765 | ||
12-4 | An Introduction to the Finite-Element Method | Exercises Set | p.777 |
12-5 | Numerical Software | Discussion Question (12-5) | p.779 |
12-4 | An Introduction to the Finite-Element Method | Discussion Question (12-4) | p.779 |
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Burden Numerical Analysis Solution Pdf
- Step 1 of 11
To construct interpolation polynomial of degree two consider allthe three nodal points
i.e.
Now take,we get
, and
We first determine the coefficient polynomial
and
Now the interpolate polynomial of degree two
taking,
- where did the x=0.45 come from?
- oh nevermind
- Step 2 of 11= 0.900447
and by using calculator
= 0.898100
Therefore the absolute error,
- this answer is incorrect. should be 1.204998
- how come should it be 1.204998?
- No moron, the answer is correct.
- nuuuuuuw
- missing the degree of 1 part.
- missing the first part where a polynomial of degree one is constructed
- Step 3 of 11
Free 32 bit games. (b) We are given with
To construct interpolation polynomial of degree one, consideronly two nodal points
Now take,we get
and
We first determine the coefficient polynomial
Now the interpolate polynomial of degree one
taking,
= 1.204159
and
= 1.198683
Therefore the absolute error,
- .441518(.45) + 1
- Therefore, absolute error must equal approximately 1.005476
- no you are wrong the absolute error is 0.005476.
- Given answer is correct though they forgot to show the +1 it is still computed. .441518(.45) = 0.1986831 0.1986831+1 = 1.198
- Step 4 of 11
To construct interpolation polynomial of degree two consider allthe three nodal points
i.e.
Now take,we get
, and
We first determine the coefficient polynomial
and
- Step 5 of 11
Now the interpolate polynomial of degree two
and by using calculator
= 1.203423
taking,
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= 1.204159
Therefore the absolute error,
- Step 6 of 11
(c) We are given with
To construct interpolation polynomial of degree one, consideronly two nodal points
Now take,we get
and
We first determine the coefficient polynomial
Now the interpolate polynomial of degree one
taking,
= 0.371563
and
= 0.352502
Therefore the absolute error,
= 0.019062
- wouldn't x_1 and x_2 give a better approximation
- nah, the values you choose for representing P1(x) must consist 0.45 in them. as in this example: 0.45 belong to (0,0.6)
- Step 7 of 11
To construct interpolation polynomial of degree two consider allthe three nodal points
i.e.
Now take,we get
, and
We first determine the coefficient polynomial
- Step 8 of 11
and
Now the interpolate polynomial of degree two
taking,
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= 0.371563
and by using calculator
= 0.368291
Therefore the absolute error,
- small mistake here subtract |.368291-.371563|
- Step 9 of 11
(d) We are given with
To construct interpolation polynomial of degree one, consideronly two nodal points
Now take,we get
and
We first determine the coefficient polynomial
Now the interpolate polynomial of degree one
taking,
= 0.483055
and
= 0.513103
- Step 10 of 11
- Step 11 of 11
Invaders from the planet moolah free download. To construct interpolation polynomial of degree two consider allthe three nodal points
i.e.
Now take,we get
, and
We first determine the coefficient polynomial
and
Now the interpolate polynomial of degree two
taking,
= 0.483055
and by using calculator
= 0.454614
Therefore the absolute error,