When dense matrix computations are too large to fit in cache, previous research proposes tiling to reduce or eliminate capacity misses. This paper presents a new algorithm for choosing problem-size dependent tile sizes based on the cache size and cache line size for a direct-mapped cache. The algorithm eliminates both capacity and self-interference misses and reduces cross-interference misses. We measured simulated miss rates and execution times for our algorithm and two others on a variety of problem sizes and cache organizations. At higher set associativity, our algorithm does not always achieve the best performance. However on direct-mapped caches, our algorithm improves simulated miss rates and measured execution times when compared with previous work.