Related papers: Performance evaluation of accelerated complex mult…
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…
Multiple-precision floating-point branch-free algorithms can significantly accelerate multi-component arithmetic implemented by combining hardware-based binary64 and binary32, particularly for triple- and quadruple-precision computations.…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our…
An exact arithmetic, memory efficient direct solution method for finite element method (FEM) computations is outlined. Unlike conventional black-box or low-rank direct solvers that are opaque to the underlying physical problem, the proposed…
A parallel direct solution approach based on domain decomposition method (DDM) and directed acyclic graph (DAG) scheduling is outlined. Computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix…
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…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
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…
The objective of this study is to present a novel, efficient, and fast direct method for solving linear systems of equations whose coefficient matrix is a tridiagonal Quasi-Toeplitz matrix. Such matrices are frequently encountered in the…
Current Python programming environment does not have any reliable and efficient multiple precision floating-point (MPF) arithmetic except ``mpmath" and ``gmpy2" packages based on GNU MP(GMP) and MPFR libraries. Although it is well known…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
Vortex element methods are often used to efficiently simulate incompressible flows using Lagrangian techniques. Use of the FMM (Fast Multipole Method) allows considerable speed up of both velocity evaluation and vorticity evolution terms in…
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…
Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…
Multi-directional 3D printing has the capability of decreasing or eliminating the need for support structures. Recent work proposed a beam-guided search algorithm to find an optimized sequence of plane-clipping, which gives volume…
Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…
Multiple patterning lithography (MPL) is regarded as one of the most promising ways of overcoming the resolution limitations of conventional optical lithography due to the delay of next-generation lithography technology. As the feature size…
This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of…