Explanation: Inherent instability is the Instability due to ill conditioned set of equations. The linear system is called ill conditioned, if small changes in the coefficients of equations result in small changes in the values of the unknowns.,
Gauss elimination method is used to solve a system of linear equations. Let's recall the definition of these systems of equations. A system of linear equations is a group of linear equations with various unknown factors. As we know, unknown factors exist in multiple equations.
Gauss-Jordan Elimination is an algorithm that can be used to solve systems of linear equations and to find the inverse of any invertible matrix. It relies upon three elementary row operations one can use on a matrix: Swap the positions of two of the rows. Multiply one of the rows by a nonzero scalar.
Explanation: Inherent instability is the Instability due to ill conditioned set of equations. The linear system is called ill conditioned, if small changes in the coefficients of equations result in small changes in the values of the unknowns.
Advantages of secant method: 1. It converges at faster than a linear rate, so that it is more rapidly convergent than the bisection method. 2. It does not require use of the derivative of the function, something that is not available in a number of applications.
Inherent instability occurs when, during a numerical step by step solution, errors generated by any means (truncation or round-off) are magnified until the true solution is swamped.
SOLUTION. Gauss elimination method: this method is used for solving linear simultaneous equations. This method is called direct method because in this method, the unknowns are eliminated successively and the system is reduced to an upper triangular system from which the unknowns are founded by back substitution.
The basic direct method for solving linear systems of equations is Gaussian elimination. The bulk of the algorithm involves only the matrix A and amounts to its decomposition into a product of two matrices that have a simpler form. This is called an LU decomposition.17-Dec-2008
What is the primary drawback of using direct methods of solution? Explanation: The drawback of using direct methods of solution is that these methods yield solution after a certain amount of fixed computation. There are no calculations and back substitution in direct methods.