Non-Linear Algebraic Equations

Question 1

the location of the sign change and consequently the root is identified more precisely by dividing the interval into a number of?

Answer 1

subintervals

Question 2

other terms for bisection method

Answer 2

binary chopping, internal halving, and Bolzano’s method

Question 3

other terms for successive substitution method?

Answer 3

fixed point iteration and one-point iteration

Question 4

secant method defines the derivative by a

Answer 4

backward finite difference

Question 5

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?

Answer 5

less than 0

Question 6

in secant method, how many estimates of x are required?

Answer 6

two

Question 7

The values of x are called the

Answer 7

roots of an equation

Question 8

In this method, two initial estimates of x are required

Answer 8

secant method

Question 9

It is the most widely used for all root locating
formulas.

Answer 9

newton-raphson method

Question 10

It is one type of incremental search method in which the interval is always divided in half

Answer 10

bisection method

Question 11

It defines the derivative by a backward finite difference.

Answer 11

secant method

Question 12

If f(xl) f(xr) = 0, the root is?

Answer 12

xr

Question 13

It is alternatively called fixed point iteration or one-point iteration

Answer 13

successive substitution method

Question 14

This method capitalizes on this observation by locating an interval where the function changes sign

Answer 14

incremental search method

Question 15

If f(xl) f(xr) < 0, then the root lies in the?

Answer 15

lower subinterval

Question 16

numerical approximation is a systematic trial and error method, and approximation method, in particular an?

Answer 16

iteration method

Question 17

4 methods in solving non-linear algebraic equations

Answer 17

1. bisection method
2. successive substitution method
3. newton-raphson method
4. secant method

Question 18

It is a systematic trial and error method, and approximation method, in particular an iteration method

Answer 18

numerical approximation

Question 19

This provides a formula to predict a new value of x as a function of an old value of x.

Answer 19

successive substitution method

Question 20

It is alternatively called binary chopping, internal halving or Bolzano’s method

Answer 20

bisection method

Question 21

bisection method is one type of _____________________ in which the interval is always divided in half

Answer 21

incremental search method

Question 22

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

Answer 22

successive substitution method

Question 23

The point where this
tangent ___________ the x axis usually represents an improved estimate of
the root.

Answer 23

crosses

Question 24

if 𝑓 (𝑥1) 𝑓 (𝑥𝑛) < 0, there there is at least _____ real root between x1 to xn

Answer 24

one

Question 25

The roots are also called the

Answer 25

zeros of the equation

Question 26

A solution of (1) is x=s such that?

Answer 26

f(s) = 0

Question 27

If f(xl) f(xr) > 0, the root lies in the?

Answer 27

upper subinterval

Question 28

If 𝒇 𝒙 in 𝒇 𝒙 = 0 does not
change sign between two
points, roots may still exist between the?

Answer 28

two points

Question 29

The idea behind the Newton’s method is that the _________________ is close to the curve and so its x-intercept, x2, is close to the x-intercept of the curve

Answer 29

tangent line

Question 30

If a function changes sign over an interval, the function value at the midpoint is evaluated

Answer 30

bisection method