Computational Methods MCQs

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1. Which of the following is NOT a numerical method?





2. Which method is used to find the roots of nonlinear equations?





3. The process of finding a numerical solution by successively refining an initial estimate is known as:





4. Which method is used to solve systems of linear equations by transforming the augmented matrix into row-echelon form?





5. Which numerical method is suitable for solving ordinary differential equations (ODEs) where the step size is relatively small?





6. What is the order of the Runge-Kutta method typically used for accurate solutions of ODEs?





7. The trapezoidal rule is used for:





8. Which method is used for solving systems of nonlinear equations iteratively?





9. Which numerical method involves dividing the interval into smaller sub-intervals to approximate the integral of a function?





10. Romberg integration improves the accuracy of numerical integration by:





11. Which method is used to find the inverse of a matrix?





12. Which iterative method is used for solving large sparse systems of linear equations?





13. Which method is used to minimize a function by iterative steps that adjust the parameters?





14. The Eigenvalue decomposition of a matrix is also known as:





15. Which method is used to solve partial differential equations (PDEs) by discretizing both time and space?





16. In numerical methods, h is often used to denote:





17. Which method is used to interpolate values between known data points?





18. The condition number of a matrix measures its:





19. Which numerical method is used to approximate the solution of integral equations?





20. Which method is used for solving nonlinear optimization problems without requiring derivatives?





21. Which method is commonly used to find the roots of a polynomial equation with complex coefficients?





22. Which numerical method is based on random sampling to compute the integral of a function?





23. The LU decomposition of a matrix A can be written as A = LU, where L is lower triangular and U is upper triangular. This decomposition is useful for:





24. Which method is used for solving nonlinear optimization problems when the objective function is not smooth?





25. In numerical methods, what does convergence refer to?





26. Which method is used for finding the eigenvalues and eigenvectors of a matrix?





27. Which method is used to approximate the derivative of a function at a point using function evaluations?





28. Which numerical method is used for smoothing data and making predictions based on polynomial interpolation?





29. Which method is used to solve linear programming problems by iteratively improving feasible solutions?





30. Which method is used to solve simultaneous nonlinear equations by transforming them into a sequence of linear equations?





31. Which method is used to solve systems of linear equations by iteratively refining the solution based on successive approximations?





32. The QR decomposition of a matrix decomposes it into:





33. Which numerical method is used for solving stiff systems of ordinary differential equations (ODEs)?





34. Which method is used for approximating the solution of a differential equation by treating derivatives as differences?





35. Which numerical method is used for finding the zeros of a function by using both function values and derivative information?





36. Which method is used for finding the roots of a polynomial equation by constructing a sequence of polynomials that have the same roots?





37. Which method is used to approximate the area under a curve by dividing it into small trapezoids?





38. Which numerical method involves solving a series of linear equations to approximate the solution of a differential equation?





39. Which method is used for minimizing a function by iteratively moving in the direction of the negative gradient?





40. Which numerical method is used for solving nonlinear systems of equations by approximating the Jacobian matrix?





41. Which method is used for finding the approximate solution of a system of linear equations by iterating over each equation and updating the variables?





42. The Householder transformation is used in numerical methods for:





43. Which method is used for solving linear programming problems by iteratively improving feasible solutions at each step?





44. Which numerical method is used for solving differential equations by discretizing the solution domain into small elements?





45. Which method is used to solve systems of linear equations by iteratively refining an initial guess until convergence?





46. The SVD (Singular Value Decomposition) of a matrix decomposes it into:





47. Which numerical method is used for finding the inverse of a matrix by decomposing it into simpler components?





48. Which method is used for finding the approximate solution of a differential equation by treating derivatives as finite differences?





49. Which method is used for finding the roots of a polynomial equation by constructing a sequence of polynomials that have the same roots?





50. Which method is used for solving systems of linear equations by iteratively refining the solution based on successive approximations?





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