Related papers: High-Performance Algorithms for Computing the Sign…
We present an optimized algorithm calculating determinant for multivariate polynomial matrix on GPU. The novel algorithm provides precise determinant for input multivariate polynomial matrix in controllable time. Our approach is based on…
We develop a systematic sign-embedding framework of operator-output quantum algorithms for matrix equations and matrix functions. Differing from the contour-integral treatment, we start with the matrix-sign embedding route: an augmented…
Recently, in-memory analog matrix computing (AMC) with nonvolatile resistive memory has been developed for solving matrix problems in one step, e.g., matrix inversion of solving linear systems. However, the analog nature sets up a barrier…
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option…
In this paper, we perform a roundoff error analysis of an integration-based method for computing the matrix sign function recently proposed by Nakaya and Tanaka. The method expresses the matrix sign function using an integral representation…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
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…
Slater basis functions have desirable properties that can improve electronic structure simulations, but improved numerical integration methods are needed. This work builds upon the SlaterGPU library for evaluation of Hamiltonian matrix…
Learning of matrix-valued data has recently surged in a range of scientific and business applications. Trace regression is a widely used method to model effects of matrix predictors and has shown great success in matrix learning. However,…
A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…
In this paper, we propose a new first-order gradient-based algorithm to train deep neural networks. We first introduce the sign operation of stochastic gradients (as in sign-based methods, e.g., SIGN-SGD) into ADAM, which is called as…
In decision-making systems, algorithmic recourse aims to identify minimal-cost actions to alter an individual features, thereby obtaining a desired outcome. This empowers individuals to understand, question, or alter decisions that…
Matrix multiplication is a fundamental kernel in high performance computing. Many algorithms for fast matrix multiplication can only be applied to enormous matrices ($n>10^{100}$) and thus cannot be used in practice. Of all algorithms…
Achieving completeness in the motion planning problem demands substantial computation power, especially in high dimensions. Recent developments in parallel computing have rendered this more achievable. We introduce an embarrassingly…
We explore new approaches for finding matrix multiplication algorithms in the commutative setting by adapting the flip graph technique: a method previously shown to be effective for discovering fast algorithms in the non-commutative case.…
The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…
We study the problem of computing matrix chain multiplications in a distributed computing cluster. In such systems, performance is often limited by the straggler problem, where the slowest worker dominates the overall computation latency.…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
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…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…