Numerical Analysis Burden Solutions Manual 9th Edition Download

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Chapter 1

Mathematical Preliminaries And Error Analysis

1-1Review of CalculusExercises Setp.11
Discussion Questionp.14
1-2Round-off-Errors and Computer ArithmeticExercises Setp.25
Discussion Questionp.29
1-3Algorithms and ConvergenceExercises Setp.35
Discussion Questionp.38
1-4Numerical SoftwareDiscussion Questionp.44

Chapter 2

Solutions Of Equations In One Variable

2-1The Bisection MethodExercises Setp.53
Discussion Questionp.54
2-2Fixed-Point IterationExercises Setp.63
Discussion Questionp.66
2-3Newton's Method and Its ExtensionsExercises Setp.74
Discussion Questionp.78
2-4Error Analysis for Iterative MethodsExercises Setp.84
Discussion Questionp.85
2-5Accelerating ConvergenceExercises Setp.89
Discussion Questionp.91
2-6Zeros of Polynomials and Muller's MethodExercises Setp.99
Discussion Questionp.100
2-7Numerical Software and Chapter ReviewDiscussion Questionp.101

Chapter 3

Interpolation And Polynomial Approximation

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3-1Interpolation and the Lagrange PolynomialExercises Setp.112
Discussion Questionp.115
3-2Data Approximation and Neville's MethodExercises Setp.120
Discussion Questionp.122
3-3Divided DifferencesExercises Setp.130
Discussion Questionp.133
3-4Hermite InterpolationExercises Setp.139
Discussion Questionp.141
3-5Cubic Spline InterpolationExercises Setp.158
Discussion Questionp.162
3-6Parametric CurvesExercises Setp.167
Discussion Questionp.168
3-7Numerical Software and Chapter ReviewDiscussion Questionp.169

Chapter 4

Numerical Differentiation And Integration

Numerical Analysis Burden Solutions Manual 9th Edition Download Full

4-1Numerical DifferentiationExercises Setp.180
Discussion Questionp.183
4-2Richardson's ExtrapolationExercises Setp.189
Discussion Questionp.191
4-3Elements of Numerical IntegrationExercises Setp.200
Discussion Questionp.201
4-4Composite Numerical IntegrationExercises Setp.208
Discussion Questionp.211
4-5Romberg IntegrationExercises Setp.217
Discussion Questionp.219
4-6Adaptive Quadrature MethodsExercises Setp.226
Discussion Questionp.228
4-7Gaussian QuadratureExercises Setp.234
Discussion Questionp.235
4-8Multiple IntegralsExercises Setp.248
Discussion Questionp.250
4-9Improper IntegralsExercises Setp.255
Discussion Questionp.256
4-10Numerical Software and Chapter ReviewDiscussion Questionp.257

Chapter 5

Initial-Value Problems For Ordinary Differential Equations

5-1The Elementary Theory of Initial-Value ProblemsExercises Setp.264
Discussion Questionp.265
5-2Euler's MethodExercises Setp.272
Discussion Questionp.275
5-3Higher-Order Taylor MethodsExercises Setp.280
Discussion Questionp.282
5-4Runge-Kutta MethodsExercises Setp.291
Discussion Questionp.293
5-5Error Control and the Runge-Kutta-Fehlberg MethodExercises Setp.300
Discussion Questionp.302
5-6Multistep MethodsExercises Setp.314
Discussion Questionp.316
5-7Variable Step-Size Multistep MethodsExercises Setp.321
Discussion Questionp.322
5-8Extrapolation MethodsExercises Setp.329
Discussion Questionp.330
5-9Higher-Order Equations and Systems of Differential EquationsExercises Setp.337
Discussion Questionp.339
5-10StabilityExercises Setp.348
Discussion Questionp.349
5-11Stiff Differential EquationsExercises Setp.355
Discussion Question (5-11)p.356
5-12Numerical SoftwareDiscussion Question (5-12)p.357

Chapter 6

Direct Methods For Solving Linear Systems

6-1Linear Systems of EquationsExercises Setp.371
Discussion Questionp.375
6-2Pivoting StrategiesExercises Setp.383
Discussion Questionp.385
6-3Linear Algebra and Matrix InversionExercises Setp.394
Discussion Questionp.400
6-4The Determinant of a MatrixExercises Setp.403
Discussion Questionp.406
6-5Matrix FactorizationExercises Setp.413
Discussion Questionp.416
6-6Special Types of MatricesExercises Setp.429
Discussion Question (6-6)p.433
6-7Numerical SoftwareDiscussion Question (6-7)p.433
Numerical Analysis Burden Solutions Manual 9th Edition Download

Chapter 7

Iterative Techniques In Matrix Algebra

7-1Norms of Vectors and MatricesExercises Setp.447
Discussion Questionp.449
7-2Eigenvalues and EigenvectorsExercises Setp.454
Discussion Questionp.456
7-3The Jacobian and Gauss-Siedal Iterative TechniquesExercises Setp.465
Discussion Questionp.468
7-4Relaxation Techniques for Solving Linear SystemsExercises Setp.473
Discussion Questionp.476
7-5Error Bounds and Iterative RefinementExercises Setp.484
Discussion Questionp.486
7-6The Conjugate Gradient MethodExercises Setp.499
7-7Numerical SoftwareDiscussion Question (7-7)p.504
7-6The Conjugate Gradient MethodDiscussion Question (7-6)p.504

Chapter 8

Approximation Theory

8-1Discrete Least Squares ApproximationExercises Setp.514
Discussion Questionp.517
8-2Orthogonal Polynomials and Least Squares ApproximationExercises Setp.524
Discussion Questionp.525
8-3Chebyshev Polynomials and Economization of Power SeriesExercises Setp.534
Discussion Questionp.535
8-4Rational Function ApproximationExercises Setp.544
Discussion Questionp.545
8-5Trigonometric Polynomial ApproximationExercises Setp.553
Discussion Questionp.555
8-6Fast Fourier TransformsExercises Setp.565
8-7Numerical SoftwareDiscussion Question (8-7)p.567
8-6Fast Fourier TransformsDiscussion Question (8-6)p.567

Chapter 9

Approximating Eigenvalues

9-1Linear Algebra and EigenvaluesExercises Setp.576
Discussion Questionp.578
9-2Orthogonal Matrices and Similarity TransformationsExercises Setp.582
Discussion Questionp.585
9-3The Power MethodExercises Setp.599
Discussion Questionp.602
9-4Householder's MethodExercises Setp.609
Discussion Questionp.610
9-5The QR AlgorithmExercises Setp.621
Discussion Questionp.624
9-6Singular Value DecompositionExercises Setp.636
Discussion Question (9-6)p.637
9-7Numerical SoftwareDiscussion Question (9-7)p.638

Chapter 10

Numerical Solutions Of Nonlinear Systems Of Equations

10-1Fixed Points for Functions of Several VariablesExercises Setp.648
Discussion Questionp.651
10-2Newton's MethodExercises Setp.655
Discussion Questionp.658
10-3Quasi-Newton MethodsExercises Setp.664
Discussion Questionp.666
10-4Steepest Descent TechnologiesExercises Setp.672
Discussion Questionp.673
10-5Homotopy and Continuation MethodsExercises Setp.680
10-6Numerical SoftwareDiscussion Question (10-6)p.682
10-5Homotopy and Continuation MethodsDiscussion Question (10-5)p.682

Chapter 11

Boundary-Value Problems For Ordinary Differential Equations

11-1The Linear Shooting MethodExercises Setp.692
Discussion Questionp.693
11-2The Shooting Method for Nonlinear ProblemsExercises Setp.699
Discussion Questionp.699
11-3Finite-Difference Methods for Linear ProblemsExercises Setp.704
Discussion Questionp.706
11-4Finite-Difference Methods for Nonlinear ProblemsExercises Setp.711
Discussion Questionp.712
11-5The Rayleigh-Ritz MethodExercises Setp.726
11-6Numerical SoftwareDiscussion Question (11-6)p.728
11-5The Rayleigh-Ritz MethodDiscussion Question (11-5)p.728

Chapter 12

Numerical Solutions To Partial Differential Equations

12-1Elliptic Partial Differential EquationsExercises Setp.741
Discussion Questionp.743
12-2Parabolic Partial Differential EquationsExercises Setp.754
Discussion Questionp.757
12-3Hyperbolic Partial Differential EquationsExercises Setp.763
Discussion Questionp.765
12-4An Introduction to the Finite-Element MethodExercises Setp.777
12-5Numerical SoftwareDiscussion Question (12-5)p.779
12-4An Introduction to the Finite-Element MethodDiscussion 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,