Index

Symbols

\ see backslash

A

algorithm

asymptotic asymptotic notation

B

backslash, [1], [2] backward error, [1], [2] in linear system

backward substitution, [1] bandwidth, [1] big-O

C

cardinal functions, [1], [2] Cholesky factorization comprehension, [1] condition number of a matrix, [1] of elementary functions of initial-value problems of interpolation, [1] of linear least squares of linear system of normal equations of rootfinding

contraction mapping convergence rate linear quadratic superlinear copy cubic spline CubicSplineInterpolation

D

data fitting by straight line nonlinear power law

DifferentialEquations discretization double precision

E

end	Euler's method, [1], [2] extrapolation, [1]

F

finite difference finite differences, [1] fit fixed point iteration, [1] fixed point problem, [1] float

floating point numbers, [1] floating-point numbers flops, [1] forward substitution, [1] Frobenius norm function

G

Gauss--Newton method, [1] Gaussian elimination, [1]

generating polynomials, [1], [2] global error Gregory integration formula

H

hat functions, [1]

hermitian, [1] Householder reflector

I

identity matrix, [1] IEEE 754, [1] ill-conditioned implicit induced matrix norm InexactError initial-value problem, [1] one-step method for solving inner product

instability of a mutistep formula interpolation, [1], [2], [3] by piecewise polnyomials by piecewise polynomials, [1], [2] by polynomials, [1], [2], [3], [4] inv inverse invertible

J

Jacobian matrix, [1]

L

least squares, [1] linear convergence, [1] linear least squares problem, [1] LinearInterpolation

Lipschitz condition local extrapolation local truncation error logistic equation, [1] LU factorization

M

machine epsilon in double precision mantissa matrix condition number matrix factorization Cholesky LU, [1] PLU QR, [1]

matrix inverse multistep multistep method, [1] implementation of

N

NaN Newton's method, [1], [2] Newton--Cotes formula, [1] nlsolve Nodes nonlinear least squares

nonlinear least squares problem norm, [1] Frobenius matrix vector, [1] normal equations, [1], [2], [3] numerical integration, [1]

O

ODEProblem ONC matrix, [1] ones opnorm order of accuracy, [1] of a finite difference formula of a multistep IVP formula of a one-step IVP solver

orthogonal, [1] matrix, [1], [2] vectors orthogonal matrix orthonormal, [1] overdetermined overflow

P

permutation matrix pinv pivoting, [1], [2]

PLU factorization predator--prey model pseudoinverse, [1]

Q

qr QR factorization

quadratic convergence, [1] Quasi-Newton methods

R

residual, [1], [2], [3] rootfinding problem roots nonsimple, [1]

row pivoting Runge--Kutta Runge--Kutta method, [1], [2]

S

secant method, [1] significand see mantissa significant digits simple root Simpson formula Simpson's formula size solve sparse sparse matrix

SPD matrix see symmetric positive definite matrix spy stability step size stiff stiff differential equation subtractive cancellation, [1], [2], [3], [4], [5] superlinear convergence, [1] symmetric matrix, [1], [2], [3] symmetric positive definite matrix, [1]

T

trapezoid formula for integration triangular matrix, [1] tridiagonal matrix, [1]

truncation error of a finite difference formula of a multistep IVP formula of a one-step IVP solver

U

underflow unit roundoff see machine epsilon

unit triangular matrix, [1] unit vector, [1] unstable

V

Vandermonde matrix, [1], [2]

Z

zero-stability

zeros