How does the way data are stored in computer memory affect the speed of numerical programs?

In numerical analysis, the way data is stored in computer memory significantly impacts the performance of numerical programs, particularly when solving large-scale problems in linear algebra.1

Understanding how elements of an array or vector are organized in memory allows for more efficient data transfer between memory and the computer's arithmetic registers. Optimizing this access pattern reduces latency, which is essential because modern computers utilize a memory hierarchy ranging from fast, small cache memory to slower, larger storage.12

Furthermore, numerical algorithms must be tailored to the specific architecture of the machine, such as whether it employs parallel processing or pipelining. By aligning data structures with the hardware's memory access patterns and processing capabilities, developers can achieve faster execution times, even on machines with similar clock speeds.1