matrix operations on large matrices on limited memory

I need to do some matrix operations on my computer. These matrices are large 1000000x1000000 and more, some operations requiring TB of memory. Obviously these cannot be d开发者_JAVA百科irectly loaded into memory and computed. What approaches can I use to solve these matrices on my computer? Assuming that the matrices cannot be reduced further using matrix optimizations and are already stored in compact form. I am thinking about using some memory mapped scheme but need some ideas.

Two suggestions:

1. Use the mmap2 system call to map the files containing both the input and output data. This allows you to map files up to 2^44 bytes and treat them as if they were already in memory. I.e. you just use a standard pointer syntax to access the data and the OS takes care of either reading or writing it from / to disk without you needing to worry about it. Not only that, but mmap is many times significantly faster than manual file I/O - See this SO post.

2. Read "What every programmer should know about memory" by Ulrich Drepper. One of the example problems he deals with is highly optimizing matrix operations.