Memory-Efficient Two-Pass Lanczos Algorithm Implementation in Rust
By
lukefleed
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Summary
This technical article presents a memory-efficient implementation of the Lanczos algorithm in Rust, addressing the significant memory requirements of the standard method. The author explores a two-pass variant that reduces memory usage from O(n×k) to O(n) at the cost of doubling matrix-vector products, demonstrating how careful implementation can make this trade-off more favorable than theoretical analysis suggests. The article focuses on algorithm engineering and low-level optimization details for high-performance computing applications.
Key quotes
· 4 pulledThe standard Lanczos method for computing matrix functions has a brutal memory requirement: storing an n×k basis matrix that grows with every iteration.
In this post, we will explore one of the most straightforward solutions to this problem: a two-pass variant of the Lanczos algorithm that only requires O(n) memory at the cost of doubling the number of matrix-vector products.
The surprising part is that when implemented carefully, the two-pass version isn't just memory-efficient—it can be surprisingly performant despite the theoretical trade-off.
How a bit of algorithm engineering and low-level details can alter what seems like a straightforward trade-off on a blackboard.
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