 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 9270 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.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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).

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).