An Inverse-free Krylov Subspace Method For Solving Eigenvalue Problems

Matrix eigenvalue problems which is one of the main branch in numerical algebra area has gainbroadly application in engineering computation and modern discipline. Therefore, to study the waysfor solving the matrix eigenvalue has important theoretical significance and application value.Inverse-free Krylov subspace methods is one of the effective ways for solving the extremeeigenvalue of generalized symmetric eigenvalue problems. Golub present an Inverse-free Krylovsubspace method which is used to avoid the difficulty calculating the Inverse matrix. Based their work,we come up with an Inverse-free Krylov subspace method with shift matrix aimed at computinginterior eigenvalue, investigating the formation of orthogonal basis, the convergence and algorithm.Moreover, in order to reduce the computational cost, we also exploit a block method for solvingmultiple interior eigenvalues that based on above. Finally, we compare the two methods by numericalexperiments and show that the proposed algorithm is efficient.