2018 Numerical Linear Algebra Lab #1 Corrected
Due Oct. 11. Turn in the program listing and output.
1. First, download the matrix ck656.mtx from the Matrix Market Collection. http://math.nist.gov/MatrixMarket
It is NEP collection, CHUCK set. It is real unsymmetric, and nonsingular. The matrix The first line contains the name of the matrix, second line, the number of rows and columns, and number of nonzero entries. Then, for each nonzero entry, the row, column, and the value. It is Matrix Market Coordinate Format.
Write a program in Fortran in double precision to
a) Compute A X = b, where A is the CK656 matrix and b is the vector consisting of all 1’s. Print X(1), and X(656).
b) Compute . Print .
c) Compute all the eigenvalues and eigenvectors. Print the
largest and smallest eigenvalue.
d) Find the SVD of A. Print the largest and smallest singular value.
e) Find the Upperhessenberg form of A, and print the first, and last diagonals of the upperhessenberg form.
f) Find the QR decomposition of A, and print the first and last
diagonal values R matrix. (R is uppertriangular, and )
To do so, browse the www for the proper routine, in Fortran or JAVA. In Fortran, you can download from
www.netlib.org
Probably Lapack has all the necessary routines.