 Chapter 1.1: Review of Calculus
 Chapter 1.2: Roundoff Errors and Computer Arithmetic
 Chapter 1.3: Algorithms and Convergence
 Chapter 10.1: Fixed Points for Functions of Several Variables
 Chapter 10.2: Newton's Method
 Chapter 10.3: QuasiNewton Methods
 Chapter 10.4: Steepest Descent Techniques
 Chapter 10.5: Homotopy and Continuation Methods
 Chapter 11.1: The Linear Shooting Method
 Chapter 11.2: The Shooting Method for Nonlinear Problems
 Chapter 11.3: FiniteDifference Methods for Linear Problems
 Chapter 11.4: FiniteDifference Methods for Nonlinear Problems
 Chapter 11.5: The RayleighRitz Method
 Chapter 12.1: Elliptic Partial Differential Equation
 Chapter 12.2: Parabolic Partial Differential Equation
 Chapter 12.3: Hyperbolic Partial Differential Equations
 Chapter 12.4: An Introduction to the FiniteElement Method
 Chapter 2.1: The Bisection Method
 Chapter 2.2: FixedPoint Iteration
 Chapter 2.3: Newton's Method and Its Extensions
 Chapter 2.4: Error Analysis for Iterative Methods
 Chapter 2.5: Accelerating Convergence
 Chapter 2.6: Zeros of Polynomials and Muller's Method
 Chapter 3.1: Interpolation and the Lagrange Polynomial
 Chapter 3.2: Data Approximation and Neville's Method
 Chapter 3.3: Divided Differences
 Chapter 3.4: Hermite Interpolation
 Chapter 3.5: Cubic Spline Interpolation1
 Chapter 3.6: Parametric Curves
 Chapter 4.1: Numerical Differentiation
 Chapter 4.10: Numerical Software and Chapter Review
 Chapter 4.2: Richardson's Extrapolation
 Chapter 4.3: Elements of Numerical Integration
 Chapter 4.4: Composite Numerical Integration
 Chapter 4.5: Romberg Integration
 Chapter 4.6: Adaptive Quadrature Methods
 Chapter 4.7: Gaussian Quadrature
 Chapter 4.8: Multiple Integrals
 Chapter 4.9: Improper Integrals
 Chapter 5.1: The Elementary Theory of InitialValue Problems
 Chapter 5.10: Stability
 Chapter 5.11: Stiff Differential Equations
 Chapter 5.12: Numerical Software
 Chapter 5.2: Euler's Method
 Chapter 5.3: HigherOrder Taylor Methods
 Chapter 5.4: RungeKutta Methods
 Chapter 5.5: Error Control and the RungeKuttaFehlberg Method
 Chapter 5.6: Multistep Method
 Chapter 5.7: Variable StepSize Multistep Methods
 Chapter 5.8: Extrapolation Methods
 Chapter 5.9: HigherOrder Equations and Systems of Differential Equations
 Chapter 6.1: Linear Systems of Equations
 Chapter 6.2: Pivoting Strategies
 Chapter 6.3: Linear Algebra and Matrix Inversion
 Chapter 6.4: The Determinant of a Matrix
 Chapter 6.5: Matrix Factorization
 Chapter 6.6: Special Types of Matrices
 Chapter 6.7: Numerical Software
 Chapter 7.1: Norms of Vectors and Matrices
 Chapter 7.2: Eigenvalues and Eigenvectors
 Chapter 7.3: The Jacobi and GaussSiedel Iterative Techniques
 Chapter 7.4: Relaxation Techniques for Solving Linear Systems
 Chapter 7.5: Error Bounds and Iterative Refinement
 Chapter 7.6: The Conjugate Gradient Method
 Chapter 8.1: Discrete Least Squares Approximation
 Chapter 8.2: Orthogonal Polynomials and Least Squares Approximation
 Chapter 8.3: Chebyshev Polynomials and Economization of Power Series
 Chapter 8.4: Rational Function Approximation
 Chapter 8.5: Trigonometric Polynomial Approximation
 Chapter 8.6: Fast Fourier Transforms
 Chapter 9.1: Linear Algebra and Eigenvalues
 Chapter 9.2: Orthogonal Matrices and Similarity Transformations
 Chapter 9.3: The Power Method
 Chapter 9.4: Householder's Method
 Chapter 9.5: The QR Algorithm
 Chapter 9.6: Singular Value Decomposition
Numerical Analysis 10th Edition  Solutions by Chapter
Full solutions for Numerical Analysis  10th Edition
ISBN: 9781305253667
Numerical Analysis  10th Edition  Solutions by Chapter
Get Full SolutionsNumerical Analysis was written by and is associated to the ISBN: 9781305253667. This textbook survival guide was created for the textbook: Numerical Analysis, edition: 10. Since problems from 76 chapters in Numerical Analysis have been answered, more than 20545 students have viewed full stepbystep answer. The full stepbystep solution to problem in Numerical Analysis were answered by , our top Math solution expert on 03/16/18, 03:24PM. This expansive textbook survival guide covers the following chapters: 76.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Outer product uv T
= column times row = rank one matrix.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.