Solve the system of equations
by LU decomposition method and find the inverse of the coefficient matrix
The solution to the system of equations using LU decomposition is: \[ x _____ _________ _________ ______ ___.
________ __________ _________ __________ _______ ___ ___.
_______ ________ _________ ____ ___ _________ ___ ______ _________ ______ __________.
_________ _______ _____ ____ ____ ______ ________ _____ _________ ___.
___ ________ ____ __________ __________ __________ __________ _____.
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For the linear system of equations
set up the Gauss-Jacobi and Gauss-Seidal iteration schemes in matrix form. Also check the convergence of the two schemes.
The function (x) = ln(1+x) is to be tabulated at equispaced points in the interval [2, 3] using linear interpolation. Find the largest step size h that can be used so that the error
in magnitude.
The equation has two real roots p and q such that | p |
| q | . If we use the fixed point iteration
, to find a root then to which root does it converge?
Using as an initial approximation find an approximation to one of the zeros of
by using Birge-Vieta method. Perform two iterations.
Find the largest real root a of lying between 1 and 2. Perform three iterations by
i) bisection method
ii) secant method ( 2, 1
Show that is a solution of the difference equation
Determine the constants in the differentiation formula
so that the method is of the highest possible order. Find the order and the error term of the method.