Notation:

Approximation: relative precision

initial

successive

Convergence = fixed point: rate, properties, order, tolerance

quadratic

linear+

Error <> attainable accuracy: asymptotic constant, conditioning

Function: evaluation, intersection with X-axis, continuity, derivative

non-linear

linear+

Interval = containment: length, left boundary point, right boundary point

bracketed

closed

open

containing root

Iteration = step

one-point

+multiple point

Point: +x coordinate, +y coordinate

boundary

left

right

mid

root

simple

multiple

Root Finder: candidate point generator, functional evaluation, iteration, sequence of intervals, convergence, termination criteria, root, function, initial approximation,successive approximations method, sequence of iterations

multiple

polynomial

method switching

Root Finding Method: error, convergence rate

Aitken delta squared extrapolation

Bolzano’s

bisection = interval halving

Illinois algorithm

Muller’s

regula Falsi

secant

interval shrinking

inverse quadratic interpolation

Newton-Raphson

second-order

Steffensen’s

Termination criterion

check for exact match

convergence

+iteraction count