NUMERICAL ANALYSIS 10TH EDITION BY
BURDEN REVIEW PAPER 2026 COMPLETE
QUESTIONS WITH EXPERT SOLUTIONS AND
MARKING SCHEME
◉ Secant Method.
Answer: Approximates the root of the function by taking the secant
line through the last two approximation. The new guess is the point
in which the secant line intersects the x-axis.
Start with two initial approximations p₀ and p₁. The next guess, p₂, is
the x-intercept of the line joining (p₀,f(p₀) and (p₁,f(p₁).
The approximation p₃ is the x-intercept of the line joining (p₁,f(p₁))
and (p₂,f(p₂)), and so on.
◉ Method of False Position.
Answer: Combination of the Secant Method and the Bisection
Method. It uses the Bisection Method to ensure that the two
previous approximations used for the secant line have opposite
signs.
Choose initial guesses p₀ and p₁ with opposite sides (p₀*p₁ < 0).
, The next guess, p₂, is the x-intercept of the line joining (p₀,f(p₀) and
(p₁,f(p₁).
Use p₀ and p₂ or p₁ and p₂ as your next guesses. Use p₀ and p₂ if
f(p₀) and f(p₂) have opposite signs. Else, use the other option.
Continue until f(p_n)=0.
◉ Muller's Method.
Answer: A root-finding method that draws a parabola through the
three previous approximations and looks at where it intersects the
x-axis. It generally intersects at 0 or 2 points.
If there are two points, then the point nearest the last point is
chosen as the newest approximation. If there are 0 points, then there
are complex solutions.
◉ IQI (Inverse Quadratic Integration).
Answer: A root-finding method that draws a parabola in the form
x=p(y) through 3 approximations.
◉ LU Factorization.
Answer: A=LU
BURDEN REVIEW PAPER 2026 COMPLETE
QUESTIONS WITH EXPERT SOLUTIONS AND
MARKING SCHEME
◉ Secant Method.
Answer: Approximates the root of the function by taking the secant
line through the last two approximation. The new guess is the point
in which the secant line intersects the x-axis.
Start with two initial approximations p₀ and p₁. The next guess, p₂, is
the x-intercept of the line joining (p₀,f(p₀) and (p₁,f(p₁).
The approximation p₃ is the x-intercept of the line joining (p₁,f(p₁))
and (p₂,f(p₂)), and so on.
◉ Method of False Position.
Answer: Combination of the Secant Method and the Bisection
Method. It uses the Bisection Method to ensure that the two
previous approximations used for the secant line have opposite
signs.
Choose initial guesses p₀ and p₁ with opposite sides (p₀*p₁ < 0).
, The next guess, p₂, is the x-intercept of the line joining (p₀,f(p₀) and
(p₁,f(p₁).
Use p₀ and p₂ or p₁ and p₂ as your next guesses. Use p₀ and p₂ if
f(p₀) and f(p₂) have opposite signs. Else, use the other option.
Continue until f(p_n)=0.
◉ Muller's Method.
Answer: A root-finding method that draws a parabola through the
three previous approximations and looks at where it intersects the
x-axis. It generally intersects at 0 or 2 points.
If there are two points, then the point nearest the last point is
chosen as the newest approximation. If there are 0 points, then there
are complex solutions.
◉ IQI (Inverse Quadratic Integration).
Answer: A root-finding method that draws a parabola in the form
x=p(y) through 3 approximations.
◉ LU Factorization.
Answer: A=LU
