Matrices are frequently decomposed in various ways in order to meet the conditions of an application, and therefore, algorithms for doing this are very important in the field of numerical linear algebra. In the tile algorithm, it is very critical to find a tile size that is suitable for the size of the matrix and the run-time environment. Smaller tiles can generate many fine-grained tasks. This can resolve load imbalances, but it causes a decline in the performance of the level three Basic Linear Algebra Subprograms (L3 BLAS) because L3 BLAS routines show higher performance with a larger size of data. Agullo et al. presented a pruned search routine for determining the size of the tile and the width of the inner blocks for tile matrix decomposition routines. To further reduce the parameter search time, we reduce the candidates by considering the number of tasks, which varies with the tile size.