Outputs (3)

Computational graphs for matrix functions (2023)
Journal Article
Jarlebring, E., Fasi, M., & Ringh, E. (2023). Computational graphs for matrix functions. ACM Transactions on Mathematical Software, 48(4), 1-35. https://doi.org/10.1145/3568991

Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve them, and ev... Read More about Computational graphs for matrix functions.

CPFloat: A C library for simulating low-precision arithmetic (2023)
Journal Article
Fasi, M., & Mikaitis, M. (2023). CPFloat: A C library for simulating low-precision arithmetic. ACM Transactions on Mathematical Software, 49(2), 1-32. https://doi.org/10.1145/3585515

One can simulate low-precision floating-point arithmetic via software by executing each arithmetic operation in hardware and then rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standa... Read More about CPFloat: A C library for simulating low-precision arithmetic.

Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores (2023)
Journal Article
Fasi, M., Higham, N. J., Lopez, F., Mary, T., & Mikaitis, M. (2023). Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores. SIAM Journal on Scientific Computing, 45(1), https://doi.org/10.1137/21M1465032

In multiword arithmetic, a matrix is represented as the unevaluated sum of two or more lower precision matrices, and a matrix product is formed by multiplying the constituents in low precision. We investigate the use of multiword arithmetic for impro... Read More about Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores.