1. A computerized method for computing eigenvectors and eigenvalues in a high performance computing (HPC) system having a plurality of nodes, each node including one or more processing cores for executing program threads, the nodes having non-uniform memory access, the method comprising: in a first computer process, reducing a square input matrix into a band matrix, the square input matrix having a number of rows that is greater than 46,340; in a second computer process, reducing the band matrix to a tridiagonal matrix; in a third computer process, computing eigenvectors and eigenvalues of the tridiagonal matrix using multiple relatively robust representations (MRRR); in a fourth computer process, transforming the computed eigenvectors of the tridiagonal matrix into eigenvectors of the band matrix using data obtained during the second computer process; and in a fifth computer process, transforming the eigenvectors of the band matrix into eigenvectors of the input matrix using data obtained during the first computer process; wherein the first, second, and third computer processes are each dynamically scheduled for execution by a number of program threads that is separately and respectively determined, for each such process, as a function of the relative runtimes of the processes.