# Index

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | Y | Z

## B

 Bauer–Fike theorem beam equation Bessel equation,  Black–Scholes equation boundary conditions Broyden update Burgers equation

## C

 C3PO,  cardinal function, , ,  Carrier equation,  centered difference CFL condition characteristic polynomial Chebyshev equation Chebyshev points Chebyshev polynomials Clenshaw–Curtis integration collocation condition number conjugate gradients conservation law contraction mapping convergence rate Crank–Nicolson method cubic spline

## D

 D'Alembert's solution Dahlquist theorems,  data fitting degree matrix diagonal matrix, ,  diagonalizable matrix differentiation matrix, , ,  diffusion equation see heat equation dimension reduction,  Dirichlet boundary condition,  Dirichlet boundary conditions divide and conquer domain of dependence double exponential transformation

## E

 eigenvalue,  eigenvalue decomposition, ,  eigenvector

## F

 FFT (fast Fourier transform) field of values fill-in of sparse matrices finite difference finite differences, , 

## G

 GMRES Gram matrix graph graph Laplacian matrix Gregory integration formula

## H

 hermitian matrix, ,  hermitian positive definite matrix see symmetric positive definite matrix Horner's algorithm Householder reflector hyperbolic PDE

## I

 identity matrix,  IEEE 754,  image (as a matrix), ,  implicit IVP solver,  improper integral,  initial-boundary-value problem initial-value problem inner product inner product space interpolation,  inverse iteration invertible matrix

## J

 Jacobian matrix, ,  Julia

## M

 machine epsilon, ,  mantissa see significand mass matrix matrix factorization matrix inverse,  Maxwell's equations method of lines, , ,  MINRES multistep method, 

## N

 NaN Neumann boundary condition,  Newton's method, ,  nonlinear least squares norm

## O

 Obi-Wan Kenobi,  ONC matrix,  order of accuracy

## R

 Rayleigh quotient residual,  Return of the Jedi Robin boundary condition rootfinding problem, ,  roots Runge phenomenon Runge–Kutta method, , 

## S

 secant method semidiscretization shifted inverse iteration see inverse iteration shock wave significand significant digits similarity transformation Simpson's formula,  sine integral function sine–Gordon equation singular matrix singular value decomposition,  soap film sparse matrix, , , ,  SPD matrix see symmetric positive definite matrix spline (cubic spline) stability,  stability region Star Wars: A New Hope, , , , , ,  steepest descent stiff differential equation, ,  stiffness matrix subtractive cancellation, , , ,  superlinear convergence SVD see singular value decomposition Sylvester equation symmetric matrix, , ,  symmetric positive definite matrix, , 

## T

 tensor-product domain The Empire Strikes Back, , , ,  transpose,  trapezoid formula triangular matrix,  tridiagonal matrix trigonometric polynomial truncation error

## U

 unit lower triangular matrix unit roundoff unit vector

## Y

 Yoda, ,