Related papers: Faster arbitrary-precision dot product and matrix …
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer…
Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…
In this paper, we report the results obtained from the acceleration of multi-binary64-type multiple precision matrix multiplication with AVX2. We target double-double (DD), triple-double (TD), and quad-double (QD) precision arithmetic…
Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits.…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
In this paper, we present fast algorithms for the product of two multivariate polynomials in sparse representation. The bit complexity of our algorithms are studied in detail for various types of coefficients, and we derive new complexity…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic. It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many…
Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…
In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…
Matrix multiplication is the foundation from much of the success from high performance technologies like deep learning, scientific simulations, and video graphics. High level programming languages like Python and R rely on highly optimized…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Matrix multiplication is a fundamental kernel in large-scale artificial intelligence and scientific computing, but its performance on conventional electronic accelerators is increasingly constrained by memory bandwidth and energy…
We want to achieve efficiency for the exact computation of the dot product of two vectors over word-size finite fields. We therefore compare the practical behaviors of a wide range of implementation techniques using different…
Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…
The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log 2 (7) $\approx$ 2.8074.…
This article is concerned with the efficient computation of modular matrix multiplication C=AB mod p, a key kernel in computer algebra. We focus on floating-point arithmetic, which allows for using efficient matrix multiplication libraries.…