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