LIST-I LIST-II A. Gauss Seidel method I. Interpolation B. Forward Newton method II. Non-linear Differential equation C. Runge Kutta method III. Numerical Integration D. Trapezoidal rule IV. Linear algebraic equations
Choose the correct answer from the options given below:
Gauss Seidel Method for Linear Algebraic Equations
The Gauss Seidel method is an iterative algorithm primarily utilized to solve systems of linear algebraic equations. It refines the solution iteratively, using the most recently computed values of the variables in each step, which generally leads to faster convergence for certain types of systems.
Forward Newton Method in Interpolation
The Forward Newton method, often referred to as Newton's forward difference formula, is a technique used in numerical analysis for interpolation. This method constructs a polynomial that passes exactly through a given set of data points, enabling estimation of function values at intermediate points.
Runge Kutta Method for Differential Equations
The Runge Kutta method encompasses a family of powerful numerical techniques used for approximating solutions to ordinary differential equations (ODEs). It is particularly effective for problems involving non-linear differential equations, where finding exact analytical solutions can be challenging.
Trapezoidal Rule in Numerical Integration
The Trapezoidal rule is a widely applied method for approximating the value of a definite integral, falling under the umbrella of numerical integration. It approximates the area under a curve by dividing the integration interval into smaller segments and treating each segment as a trapezoid.
Summary of Method Matching
Below is a breakdown matching the methods presented in LIST-I with their corresponding applications in LIST-II:
| LIST-I Method | LIST-II Application | Key Purpose |
|---|---|---|
| A. Gauss Seidel method | IV. Linear algebraic equations | Iterative solution for linear systems. |
| B. Forward Newton method | I. Interpolation | Polynomial interpolation using differences. |
| C. Runge Kutta method | II. Non-linear Differential equation | Numerical approximation for ODEs. |
| D. Trapezoidal rule | III. Numerical Integration | Approximation of definite integrals. |
Important Questions from Mixed Topic (CUET PG)
- Kalpsutra, the illustrated canonical text is from:-
- The Harappan city almost exclusively devoted to craft production was-:
- Mohandas Karamchand Gandhi launched quit India movement after the failure of:-
- The "Objectives Resolution" was introduced in constituent assembly by:-
- Who among the following was not a member of the constituent assembly:-
