Introduction to Sparse Matrices In Scilab - Projects

}{sciprint (" %+fi", pdblImg [k ]);}sciprint ("\n");k ++;}}LhsVar (1) = 0;return 0;9 The ARnoldi PACKageARPACK is a collection of Fortran77 subroutines designed to solve largescale eigenvalue problems. The functions available in Scilab are presented inthe figure 10.The package is designed to compute a few eigenvalues and correspondingeigenvectors of a general n by n matrix A. It is most appropriate for largesparse or structured matrices A where structured means that a matrix-vectorproduct w = Av requires order n rather than the usual order n 2 floating pointoperations. This software is based upon an algorithmic variant of the Arnoldiprocess called the Implicitly Restarted Arnoldi Method (IRAM). When thematrix A is symmetric it reduces to a variant of the Lanczos process calledthe Implicitly Restarted Lanczos Method (IRLM). These variants may beviewed as a synthesis of the Arnoldi/Lanczos process with the ImplicitlyShifted QR technique that is suitable for large scale problems. For manystandard problems, a matrix factorization is not required. Only the action ofthe matrix on a vector is needed.ARPACK software is capable of solving large scale symmetric, nonsymmetric,and generalized eigenproblems from significant application areas. Thesoftware is designed to compute a few (k) eigenvalues with user specified featuressuch as those of largest real part or largest magnitude. Storage requirementsare on the order of nk locations. No auxiliary storage is required. A setof Schur basis vectors for the desired k-dimensional eigen-space is computedwhich is numerically orthogonal to working precision. Numerically accurateeigenvectors are available on request.The following is a list of the main features of the library :– Reverse Communication Interface.23