Introduction to Sparse Matrices In Scilab - Projects

The solver argument is designed so that we can customize the linear equationsolver which we want to use. For example, if we want to use the sparsebackslash operator, all we have to do is to create the mysolverBackslashfunction as below.function u= mysolverBackslash (N, b)A = scibench_poissonA (N);u = A\b;endfunctionThe following script solves the Poisson equation with N = 50.scf ();scibench_poisson (50 , %t , %t , mysolverBackslash );The previous script produces the following output, where h is the dimensionnalspacee step and enorminf is the value of the infinite norm of the error.-> scibench_poisson (50 , %t , %t , mysolverBackslash );N = 50h = 1.9607843137254902 e -002h^2 = 3.8446751249519417 e -004enorminf = 1.2634082165868810 e -003C = enorminf / h^2 = 3.2861247713424775 e +000wall clock time = 0.15 secondsThe previous script also produces the plot in the figure 13.It is then easy to use the pcg function built in Scilab, which uses a preconditionnedconjugate gradient algorithm. We use the scibench_poissonAufunction, which computes the A*u product without actually storing the matrixA.function u= mysolverPCG (N, b)tol = 0.000001;maxit = 9999;u = zeros (N ^2 ,1);[u,flag ,iter , res ] = ..pcg ( scibench_poissonAu ,b,tol , maxit ,[] ,[] ,u);endfunctionscf ();[ timesec , enorminf ,h] = ..scibench_poisson (50 , %f , %t , mysolverPCG );30