Non-Linear Algebraic Equations Flashcards
the location of the sign change and consequently the root is identified more precisely by dividing the interval into a number of?
subintervals
other terms for bisection method
binary chopping, internal halving, and Bolzanoโs method
other terms for successive substitution method?
fixed point iteration and one-point iteration
secant method defines the derivative by a
backward finite difference
Choose xl and xu as two guesses for the root such that the function changes over the interval. This can be checked by ensuring that f(xl) f(xu) is?
less than 0
in secant method, how many estimates of x are required?
two
The values of x are called the
roots of an equation
In this method, two initial estimates of x are required
secant method
It is the most widely used for all root locating
formulas.
newton-raphson method
It is one type of incremental search method in which the interval is always divided in half
bisection method
It defines the derivative by a backward finite difference.
secant method
If f(xl) f(xr) = 0, the root is?
xr
It is alternatively called fixed point iteration or one-point iteration
successive substitution method
This method capitalizes on this observation by locating an interval where the function changes sign
incremental search method
If f(xl) f(xr) < 0, then the root lies in the?
lower subinterval
numerical approximation is a systematic trial and error method, and approximation method, in particular an?
iteration method
4 methods in solving non-linear algebraic equations
- bisection method
- successive substitution method
- newton-raphson method
- secant method
It is a systematic trial and error method, and approximation method, in particular an iteration method
numerical approximation
This provides a formula to predict a new value of x as a function of an old value of x.
successive substitution method
It is alternatively called binary chopping, internal halving or Bolzanoโs method
bisection method
bisection method is one type of _____________________ in which the interval is always divided in half
incremental search method
It employs a formula to predict the root. This formula can be developed by rearranging the function f(x)= 0 so that x is on the left-hand side of the equation
successive substitution method
The point where this
tangent ___________ the x axis usually represents an improved estimate of
the root.
crosses
if ๐ (๐ฅ1) ๐ (๐ฅ๐) < 0, there there is at least _____ real root between x1 to xn
one
The roots are also called the
zeros of the equation
A solution of (1) is x=s such that?
f(s) = 0
If f(xl) f(xr) > 0, the root lies in the?
upper subinterval
If ๐ ๐ in ๐ ๐ = 0 does not
change sign between two
points, roots may still exist between the?
two points
The idea behind the Newtonโs method is that the _________________ is close to the curve and so its x-intercept, x2, is close to the x-intercept of the curve
tangent line
If a function changes sign over an interval, the function value at the midpoint is evaluated
bisection method
