Introduction to Sparse Matrices In Scilab - Projects

-->x= lusolve (h,b)x =1.0.50.33333330.25--> ludel (h);3.2 Sparse backslashThe backslash operator \ can be used with sparse matrices. Depending onthe size of the sparse matrix A, the statement A\b has two different meanings.– If the matrix A is square, therefore the linear system of equations Ax = bis solved. In this case, the sparse backslash uses a sparse LU decompositionto solve the problem.– If the matrix A is non square, therefore the linear least squares problemmin ‖Ax − b‖ 2 is solved. In this case, the sparse backslash uses thenormal equations and form the linear system of equations A T Ax = A T b.Then a sparse LU decomposition is used to solve the problem.In the following example, we solve a sparse 5-by-5 system of linear equations.Afull = [2 3 0 0 0;3 0 4 0 6;0 -1 -3 2 0;0 0 1 0 0;0 4 2 0 1];A = sparse ( Afull );b = sparse ([8 ; 45; -3; 3; 19]);x = A\bIn the following example, we solve a 7-by-5 overdetermined system ofequations.Afull = [2 3 0 0 03 0 4 0 60 -1 -3 2 00 0 1 0 00 4 2 0 12 -5 0 -6 312