Numerical Analysis for computer scientists

1. Consider the equation: x^5 - 4x^4 + 4x^3 = 0. (a) (4 marks) Solve the equation using hand calculations. What is the order of

1. Consider the linear system (a) (4 marks) Starting with the zero vector, use hand calculations to perform two iterations of Jacobi method.

1. Consider the linear system (a) (4 marks) Starting with the zero vector, use hand calculations to perform two iterations of Jacobi method.

1. Consider the following system (a) (5 marks) Use hand calculations to solve the system using Gaussian elimination method with no pivoting.

1. Consider the following system (a) (5 marks) Use hand calculations to solve the system using Gaussian elimination method with no pivoting.

1-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 ...

1. 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 ...

1. 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 ...

1. 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) = ...

1. 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) = ...

1. (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) ...

1. (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) ...

1. 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 ...

1. 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 ...

1. 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 ...

1. 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 ...

1. 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 ...

1. 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 ...