Related papers: Memory-Usage Advantageous Block Recursive Matrix I…
Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using…
Obtaining the inverse of a large symmetric positive definite matrix $\mathcal{A}\in\mathbb{R}^{p\times p}$ is a continual challenge across many mathematical disciplines. The computational complexity associated with direct methods can be…
We investigate effects of ordering in blocked matrix--matrix multiplication. We find that submatrices do not have to be stored contiguously in memory to achieve near optimal performance. Instead it is the choice of execution order of the…
Runtime characteristics of sparse matrix computations and related processes may be often improved by reducing memory footprints of involved matrices. Such a reduction can be usually achieved when matrices are processed in a block-wise…
$k$-diagonal circulant matrices and cyclic banded matrices are widely used in numerical simulations and signal processing of circular linear systems. Algorithms that directly involve or specify linear or quadratic complexity for the…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
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…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…
A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion…
We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parallel programs based on these algorithms on a supercomputer…
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected $O\big(n^{2.2131}\big)$ time for the current values of fast rectangular matrix multiplication. We achieve the same…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…
A new runtime environment for the execution of recursive matrix algorithms on a supercomputer with distributed memory is proposed. It is designed both for dense and sparse matrices. The environment ensures decentralized control of the…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…
Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…
We propose a novel approach to reduce memory consumption of the backpropagation through time (BPTT) algorithm when training recurrent neural networks (RNNs). Our approach uses dynamic programming to balance a trade-off between caching of…
Inspired by recent work on extended image volumes that lays the ground for randomized probing of extremely large seismic wavefield matrices, we present a memory frugal and computationally efficient inversion methodology that uses techniques…
The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the…
The report is devoted to the concept of creating block-recursive matrix algorithms for computing on a supercomputer with distributed memory and dynamic decentralized control.