Related papers: Sparse Matrix Implementation in Octave
Sparse matrix multiplication (SpMM) is widely applied to numerous domains, such as graph processing, machine learning, and data analytics. However, inner product based SpMM induces redundant zero-element computing for mismatched nonzero…
We multiply two $n \times n$ matrices $S,T$ over semirings in the Congested Clique model, where $n$ fully connected nodes communicate synchronously using $O(\log n)$-bit messages, within $O(nz(S)^{1/3} nz(T)^{1/3}/n + 1)$ rounds of…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
Fill-ins are new nonzero elements in the summation of the upper and lower triangular factors generated during LU factorization. For large sparse matrices, they will increase the memory usage and computational time, and be reduced through…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
We present a C++ header-only parallel sparse matrix library, based on sparse quadtree representation of matrices using the Chunks and Tasks programming model. The library implements a number of sparse matrix algorithms for distributed…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…
While existing algorithms may be used to solve a linear system over a general field in matrix-multiplication time, the complexity of constructing a symmetric triangular factorization (LDL) has received relatively little formal study. The…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…
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…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
Sparse matrix computation is crucial in various modern applications, including large-scale graph analytics, deep learning, and recommender systems. The performance of sparse kernels varies greatly depending on the structure of the input…
In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
We consider the task of approximating a matrix function $f(A)$, where $A$ is a matrix in which only a relatively small number of (not necessarily consecutive) sub- and superdiagonals contain nonzero entries. Approximating $f$ by a…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…
We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…