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Textbooks / Math / Numerical Analysis 9

Numerical Analysis 9th Edition - Solutions by Chapter

Numerical Analysis | 9th Edition | ISBN: 9780538733519 | Authors: Richard L. Burden, J. Douglas Faires

Full solutions for Numerical Analysis | 9th Edition

ISBN: 9780538733519

Numerical Analysis | 9th Edition | ISBN: 9780538733519 | Authors: Richard L. Burden, J. Douglas Faires

Numerical Analysis | 9th Edition - Solutions by Chapter

Solutions by Chapter
4 5 0 393 Reviews
Textbook: Numerical Analysis
Edition: 9
Author: Richard L. Burden, J. Douglas Faires
ISBN: 9780538733519

Since problems from 73 chapters in Numerical Analysis have been answered, more than 69847 students have viewed full step-by-step answer. Numerical Analysis was written by and is associated to the ISBN: 9780538733519. The full step-by-step solution to problem in Numerical Analysis were answered by , our top Math solution expert on 03/16/18, 03:30PM. This textbook survival guide was created for the textbook: Numerical Analysis, edition: 9. This expansive textbook survival guide covers the following chapters: 73.

Key Math Terms and definitions covered in this textbook
  • Cofactor Cij.

    Remove row i and column j; multiply the determinant by (-I)i + j •

  • Cramer's Rule for Ax = b.

    B j has b replacing column j of A; x j = det B j I det A

  • Cyclic shift

    S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

  • Elimination.

    A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

  • Gauss-Jordan method.

    Invert A by row operations on [A I] to reach [I A-I].

  • Hermitian matrix A H = AT = A.

    Complex analog a j i = aU of a symmetric matrix.

  • Iterative method.

    A sequence of steps intended to approach the desired solution.

  • Least squares solution X.

    The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b - Ax is orthogonal to all columns of A.

  • Length II x II.

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

  • Nullspace N (A)

    = All solutions to Ax = O. Dimension n - r = (# columns) - rank.

  • Orthogonal subspaces.

    Every v in V is orthogonal to every w in W.

  • Particular solution x p.

    Any solution to Ax = b; often x p has free variables = o.

  • Pivot columns of A.

    Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

  • Polar decomposition A = Q H.

    Orthogonal Q times positive (semi)definite H.

  • Semidefinite matrix A.

    (Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

  • Solvable system Ax = b.

    The right side b is in the column space of A.

  • Spectrum of A = the set of eigenvalues {A I, ... , An}.

    Spectral radius = max of IAi I.

  • Triangle inequality II u + v II < II u II + II v II.

    For matrix norms II A + B II < II A II + II B II·

  • Vandermonde matrix V.

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

  • Wavelets Wjk(t).

    Stretch and shift the time axis to create Wjk(t) = woo(2j t - k).