Assignment 1- Mat lab and octave -Numerical Analysis for Scientists-2019
1. Consider the following system (a) (5 marks) Use hand calculations to solve the system using Gaussian elimination method with no pivoting.
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1. Consider the following system (a) (5 marks) Use hand calculations to solve the system using Gaussian elimination method with no pivoting.
Continue reading1-Solve the system using Gaussian elimination method with partial pivoting. 2-Find all the eigenvalues of A and find the eigenvector corresponding to the dominant eigenvalue. (b) (3 marks) Perform one iteration of the power method starting with X0. (c) (1 mark) What can you ...
Continue reading1. Consider the following system (a) (10 marks) Find the LU decomposition of the coefficient matrix A and then solve the resulting triangular systems. (b) (2 marks) Do you expect that the iterations of Jacobi method for the above system will converge? Justify your ...
Continue reading1. Consider the integral (a) Using hand calculations, approximate the above integral using trapezoidal rule. (b) Using hand calculations, approximate the above integral using Simpson's rule. (c) Using hand calculations, approximate the above integral by Simpson's 3/8 rule. 2. Find the degree of precision ...
Continue reading1. Consider the data (a) (9 marks) Using hand calculations, find the least-squares line y = f(x) = Ax + B for the data and calculate the root-mean-square error E2(f). (b) (3 marks) Using Matlab, finnd the least-squares line y = f(x) = ...
Continue reading1. Consider the data (a) (9 marks) Using hand calculations, find the least-squares line y = f(x) = Ax + B for the data and calculate the root-mean-square error E2(f). (b) (3 marks) Using Matlab, finnd the least-squares line y = f(x) = ...
Continue reading1. (a) (6 marks) Find the Taylor polynomial of degree 3 for f(x) = x^(3/2) expanded about x0 = 4. (b) (2 marks) Does f(x) =x^(3/2) have a Taylor polynomial expansion about x0 = 0? Justify your answer. 2. Consider the data (a) (5 marks) ...
Continue reading1. (a) (6 marks) Find the Taylor polynomial of degree 3 for f(x) = x^(3/2) expanded about x0 = 4. (b) (2 marks) Does f(x) =x^(3/2) have a Taylor polynomial expansion about x0 = 0? Justify your answer. 2. Consider the data (a) (5 marks) ...
Continue reading1. Consider the equation: x^7 + 8x^6 + 16x^5 = 0. (a) (4 marks) Solve the equation using hand calculations. What is the order of each root of the equation? (b) (4 marks) Find an interval [a, b] such that the bisection method ...
Continue reading1. Consider the equation: x^7 + 8x^6 + 16x^5 = 0. (a) (4 marks) Solve the equation using hand calculations. What is the order of each root of the equation? (b) (4 marks) Find an interval [a, b] such that the bisection method ...
Continue reading1. Consider the system of linear equations (a) (10 marks) Use hand calculations to find the Cholesky decomposition of the coefficient matrix A and then solve the resulting triangular system. (b) (2 marks) Use Matlab built in command to find the Cholesky decomposition of ...
Continue reading1. Consider the system of linear equations (a) (10 marks) Use hand calculations to find the Cholesky decomposition of the coefficient matrix A and then solve the resulting triangular system. (b) (2 marks) Use Matlab built in command to find the Cholesky decomposition of ...
Continue reading1. Consider the following system (a) (5 marks) Use hand calculations to solve the system using Gaussian elimination method with no pivoting. (b) (7 marks) Use hand calculations to solve the system using Gaussian elimination method with partial pivoting. 2. Consider the system of linear ...
Continue reading1. Consider the following system (a) (5 marks) Use hand calculations to solve the system using Gaussian elimination method with no pivoting. (b) (7 marks) Use hand calculations to solve the system using Gaussian elimination method with partial pivoting. 2. Consider the system of linear ...
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