a-orthogonality 4-39a absolute error 2-5 accelerating convergence (aitken's) 3-14 accumulated error, ode method 6-19 adams corrector method 6-30 adams predictor method 6-30 adams-bashfort formula 6-30 adams-bashfort-moulton formula 6-31 adams-moulton formula 6-30 adjoint of a matrix 4-15 aitken's formula (accelerating converg) 3-14 algorithms, iterative 2-12 approximation, linear 5-4 approximation, non-linear 5-6 approximations 5-1 backward difference (finite difference) 5-14 bairstow's method 3-16 basis vectors 4-42a bessel's formula (central difference) 5-30 bisection root finding algorithm 3-5 block multiplication of matrices 4-7 bolzano's root finding algorithm 3-5 boundary value problem 6-17 boundary value problems 6-33a bracketing method--root finding 3-3 bracketing strategy--root finding 3-2 catostrophic cancellation 2-4 central difference (finite difference) 5-14 characteristic polynomial 4-14 characteristic value 4-13 characteristic vector 4-13 chebyshev polynomials 5-47 chebyshev polynomials, table 5-48 choleski's LU factorization 4-25 clamped boundary condition (splines) 5-39 companion matrix 4-14 complex numbers 4-15a condition and errors 2-16 condition number and error 4-34 condition number of a matrix 4-16ar condition of a problem 2-15 conjugate gradient method 4-39 conjugate transpose of a matrix 4-15 convergence 3-17 convergence rates 2-14 convergence, accelerating 3-14 converting decimal fractions to binary 2-2 coupled equations 6-18 cramer's rule for solving linear sys. 4-26 crout's LU factorization 4-25 cubic splines 5-34 cubic splines, derivation 5-36 decimal fractions to binary, converting 2-2 decimal places 2-3 density function 5-45 dependent, linearly 4-2 derivative (finite difference) 5-14 derivatives (finding) and differences 5-21 derivatives (finding) and differences 5-22 determinant 4-12 deviation (least squares) 5-3r diagonal of matrix 4-3 difference tables 5-18 difference tables and errors 5-26 differential equations 6-16 direct solution method 1-6 discretization (bvp) 6-34 discretization (bvp) 6-38 divided difference (finite difference) 5-14 divided difference interpolation form 5-32 divided differences 5-28 doolittle's LU factorization 4-25 dot product 4-4 efficiency 2-7 eigenvalues 4-13 eigenvalues, finding 4-41 eigenvalues, finding all 4-46 eigenvectors 4-13 eigenvectors, finding 4-41 elliptic pde 6-16 error analysis 2-6 error analysis, euler method 6-24 error measurement for linear system 4-33 error, absolute 2-5 error, accumulated, ode method 6-19 error, global, ode method 6-19 error, local, ode method 6-19 error, percent 2-5 error, relative 2-5 errors 2-3 errors and condition 2-16 errors and difference tables 5-26 errors, measurement 2-5 errors, sources 2-4 euler error analysis 6-24 euler method, modified 6-28 euler's method (ode) 6-20 euler's method (ode) 6-21 exponent of real number 2-1 extrapolation 5-10 factorization (matrices) 4-23 false position root finding algorithm 3-6 finite difference and odes 5-20 finite difference bvp method 6-38 finite difference calculus 5-14 finite difference operators 5-14 forward difference (finite difference) 5-14 function, numerical 1-8 gauss quadrature 6-13 gauss-jordan 4-31a gauss-seidel 4-37 gaussian elimination 4-21 gaussian elimination, operation count 4-26 gerschgorin's disk theorem 4-42 global error, ode method 6-19 gram-schmidt orthogonalization a-1 gram-schmidt process 5-46 hardware rounding 2-3 heat equation (pde) 6-16 hermitian matrix 4-15 hessenberg matrix, upper 4-46 heun's formula (RK method) 6-28 hilbert matrix 4-36 horner's rule 2-8 horner's rule 2-9 hyperbolic pde 6-16 ill-conditioned problem 2-15 independent, linearly 4-2 inherent error 2-3 initial value problem 6-17 inner product, vector 4-4 integer representation 2-1 integration 6-2 internal halving root finding algorithm 3-5 interpolating polynomial, lagrange 5-12 interpolation 5-10 interpolation 5-2 interpolation and difference operators 5-22 interpolation formulae 5-29 interpolation, polynomial 5-11 interval strategy--root finding 3-2 inverse of matrix 4-12 inverse power method 4-45 invertible matrix 4-12 iterative algorithms 2-12 iterative method 1-6 iterative solution of linear systems 4-37 jacobi's method 4-37 lagrange interpolating polynomial 5-12 laplace equation (pde) 6-16 least squares 5-3r linear algebra 4-1 linear approximation 5-4 linear convergence 2-14 linear equation 4-2 linear regression line 5-4 linear system 4-2 linear systems, backward substitution 4-19 linear systems, backward substitution 4-22 linear systems, forward elimination 4-21 linear systems, solving 4-18 linearize the curve 5-8 linearly dependent 4-2 linearly independent 4-2 local error, ode method 6-19 LU decomposition 4-23 maclaurin series 2-10 mantissa of real number 2-1 matrices, special 4-8 matrix 4-3 matrix arithmetic 4-4 matrix multiplication 4-5 matrix norm 4-16r matrix operations, analysis 4-10 matrix-vector product 4-11 mean value (finite difference) 5-14 modified euler method 6-28 multi-step ode method 6-19 multi-step ode methods 6-30 multiple roots 3-2 multiple roots (root finding) 3-13 n-th order convergence 2-14 natural spline 5-39 nested multiplication 2-9 newton backward difference formula 5-30 newton interpolating polynomial 5-32 newton's method 1-6 newton-cotes formula (integration) 6-3 newton-gregory forward difference form 5-29 newton-raphson root finding algorithm 3-8 non-linear approximations 5-6 non-singular matrix 4-12 normal equations 4-17 normal equations 5-3a norms, matrix 4-16r norms, vector 4-16r numerical function 1-8 ode 6-16 ordinary differential equations see ODE orthogonal functions 5-45 orthogonal matrices 4-15 orthogonality, a-orthogonality 4-39a orthonomal functions 5-45 over-determined linear system 4-2 parabolic pde 6-16 partial differential equations see PDE pde 6-16 percent error 2-5 pivoting, complete 4-29 pivoting, partial 4-28 pivoting, scaled 4-29 poisson eq example, discrete method 6-44 poisson equation (pde) 6-16 polynomial interpolation 5-11 polynomial, lagrange interpolating 5-12 polynomials, roots 3-16 positive definite matrices 4-17 power method (dominant eigenvalue) 4-43 preconditioning 4-39d predictor-corrector methods 6-30 QR decomposition 4-46 quadratic convergence 2-14 quadrature 6-12 quadrature, guass 6-13 real number representation 2-1 rectangle rule (midpoint rule) 6-2 regula falsi root finding algorithm 3-6 relative error 2-5 relaxation 4-38 representing numbers 2-1 residual 4-32 richardson extrapolation 6-10 richardson iteration 4-40 richardson's extrapolation 6-23 romberg integration 6-11 root finding 3-1 roots of polynomials 3-16 runge-kutta higher order method 6-29 runge-kutta methods 6-26 scaling 4-29 secant root finding algorithm 3-9 self-starting ode method 6-19 shift operator (finite difference) 5-14 shooting method 6-34 shooting method 6-35 significant digits 2-3 similar matrices 4-12 simpson's 1/3 rule (integration) 6-6 simpson's 1/3 rule error 6-8 simpson's 3/8 rule (integration) 6-9 singular matrix 4-12 singular system matrix 4-30 singular value decomposition 4-17 slope strategy--root finding 3-2 slope strategy--root finding 3-7 SOR 4-38 spectral decomposition 4-17 spectral radius of a matrix 4-16ar spectrum of a matrix 4-16ar stiefel iteration 4-40 stiff differential equations 6-33 stirling's formula (central difference) 5-30 strassen's algorithm 4-6 subdiagonal of matrix 4-3 successive over/under relaxation 4-38 superdiagonal of matrix 4-3 symmetric matrix 4-15 taylor series 2-10 taylor series (and finite difference) 5-15 taylor series ode method 6-25 tchebycheff polynomials 5-47 transpose of a matrix 4-15 trapezoidal rule (integration) 6-4 trapezoidal rule error 6-5 tschebycheff polynomials 5-47 under-determined liear system 4-2 unitary matrix 4-15 vector norm 4-16r vector product 4-4 wave equation (pde) 6-16 weight function 5-45 well-conditioned problem 2-15
This page is maintained by Dennis C. Smolarski, S.J.
dsmolarski "at" scu.edu
© Copyright 2001, 2005, 2009 Dennis C. Smolarski, SJ, All rights reserved.
Last changed: 14 December 2009.