Related papers: Matrix compression along isogenic blocks
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…
We use neural network algorithms for finding compression methods of images in the framework of iterated function systems which is a collection of the transformations of the interval $(0, 1)$ satisfying suitable properties.
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…
Many matrices associated with fast transforms posess a certain low-rank property characterized by the existence of several block partitionings of the matrix, where each block is of low rank. Provided that these partitionings are known,…
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…
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…
In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity…
Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…
A novel algorithm for creating a mathematical model of curved shapes is introduced. The core of the algorithm is based on building a graph representation of the contoured image, which occupies less storage space than produced by raster…
The computation of a matrix function $f(A)$ is an important task in scientific computing appearing in machine learning, network analysis and the solution of partial differential equations. In this work, we use only matrix-vector products…
A Maple implementation of partitioned matrices is described. A recursive block data structure is used, with all operations preserving the block abstraction. These include constructor functions, ring operations such as addition and product,…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
Morse decompositions partition the flows in a vector field into equivalent structures. Given such a decomposition, one can define a further summary of its flow structure by what is called a connection matrix.These matrices, a generalization…
In this paper we introduce compressed commuting graph of rings. It can be seen as a compression of the standard commuting graph (with the central elements added) where we identify the vertices that generate the same subring. The compression…
Graphs can be used to represent a wide variety of data belonging to different domains. Graphs can capture the relationship among data in an efficient way, and have been widely used. In recent times, with the advent of Big Data, there has…