Ch 5 Power method -Inverse power method Lab 09. Approximating Eigenvalues Approximate an eigenvalue and an associated eigenvector of a given nxn matrix A near a given value p and a nonzero vector=(x,,,n) put There are several sets of inputs. For each set: aIn The 1st line contains an integer100≥n≥0 which21、0n is the size of a matrix. n=-l signals the end of file The following n lines contain the matrix entries in the format shown: The next line contains a real number Tol. which is the tolerance for eigenvalues, and an integer N20 which is the maximum number of iterations. The next line contains an integer n2 m>0 which is the number of eigenvalues to be approximated. Each of the following m lines contains a real number p which is an initial approximation of the eigenvalue, followed by n real number entries of the nonzero vector x=(x1,…,xn The numbers are separated by spaces and new lines. The inputs guarantee that the shifted matrix can be factorized by doolittle method.Ch.5 Power Method –Inverse Power Method Lab 09. Approximating Eigenvalues Approximate an eigenvalue and an associated eigenvector of a given nn matrix A near a given value p and a nonzero vector . Input There are several sets of inputs. For each set: The 1 st line contains an integer 100  n  0 which is the size of a matrix. n = −1 signals the end of file. The following n lines contain the matrix entries in the format shown: The next line contains a real number TOL, which is the tolerance for eigenvalues, and an integer N  0 which is the maximum number of iterations. The next line contains an integer n  m > 0 which is the number of eigenvalues to be approximated. Each of the following m lines contains a real number p which is an initial approximation of the eigenvalue, followed by n real number entries of the nonzero vector . The numbers are separated by spaces and new lines. The inputs guarantee that the shifted matrix can be factorized by Doolittle method. n nn n n a a a a a a ... ... ... ... ... ... 1 21 2 11 1 T x x xn ( , ..., ) = 1  T x x xn ( , ..., ) = 1 