Floating point in Julia

Absolute and relative accuracy

Surprising arithmetic

Horner’s rule

Instability of the quadratic formula

Stable alternative to the quadratic formula

Polynomial roots

Interpolating the population of China

Vectors and matrices in Julia

Backslash for solving linear systems

Solving triangular systems

Gaussian elimination

Row operations

Using LU factorization

Timing and flop counts

Timing matrix-vector multiplication

Timing of LU factorization

Failure of plain LU factorization

Row pivoting

Vector norms

Matrix norms

Condition number bounds on error

Banded matrices

Timing for banded matrices

Symmetric LU

Cholesky factorization

Interpolating temperature data

Fitting temperature data

Convergence to \pi

Instability in the normal equations

QR factorizations in Julia

Householder QR

Roots of Bessel functions

Conditioning of roots

Fixed point iteration

Convergence of fixed point iteration

The idea of Newton’s method

Convergence of Newton’s method

Usage of newton

Using the secant line

Convergence of the secant method

Inverse quadratic interpolation

The Newton idea for systems

Usage of newtonsys

Using levenberg

Michaelis–Menten fitting

Poor conditioning in polynomial interpolation

Piecewise polynomial interpolation

Polynomial cardinal functions

Hat functions

Piecewise linear interpolation

Convergence of PL interpolation

Cubic splines

FD at arbitrary nodes

Convergence of finite differences

Comparison of 1st and 2nd order

Roundoff in finite differences

Numerical integration

Convergence of trapezoidal integration

Extrapolation for numerical integration

An oscillatory integrand

Adaptive integration

Numerical IVP solution

Using an IVP solution

IVP with singularity

Conditioning of IVPs

Convergence of Euler’s method

Matrix exponential

Predator-prey system

Convergence of RK methods

Adaptive RK

Adaptivity at a singularity

Convergence of AB4

Accuracy isn’t everything

Instability in a multistep method