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Numerical Methods: Equations Quiz

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Numerical Methods: Equations Quiz

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Numerical methods for equations

Created by

Suvalakshmi M
Suvalakshmi M
India

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Numerical Methods: Equations Quiz
 

Numerical Methods: Equations QuizOnline version

Numerical methods for equations

by Suvalakshmi M
1

Which condition guarantees a root exists in the Bisection Method?

2

In the Regula Falsi (False Position) method, the next x value is found where the straight line through (a,f(a)) and (b,f(b)) crosses the axis. What is the formula for x_r?

3

Newton–Raphson update formula is: x_{n+1} = ?

4

Gauss Elimination aims to transform the coefficient matrix to which form before back substitution?

5

How does Gauss–Seidel differ from Jacobi iteration for solving Ax=b?

6

What is meant by the rate of convergence in iterative methods?

7

Convergence of Gauss–Seidel is guaranteed for which type of matrices?

8

Which equation type is especially suited for Newton–Raphson when derivatives are easy to compute?

9

What is a common stopping criterion for iterative root-finding methods?

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A sign change in the interval implies a root by the Intermediate Value Theorem.

x_r is the x-intercept of the line joining (a,f(a)) and (b,f(b)).

Iterative root-finding using tangent line approximation.

Standard Gauss elimination leads to row-echelon form; Gauss-Jordan continues to reduced form.

Jacobi uses the previous iteration vector entirely; Gauss-Seidel uses newest components immediately.

Typical measures are order p and asymptotic error constant.

SPD matrices ensure convergence of Gauss–Seidel under standard norms.

Newton–Raphson leverages f'(x) readily for fast quadratic convergence.

Convergence is declared when successive iterates change by less than a tolerance.

 
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