Related papers: A New Recursive Algorithm For Inverting A General …
A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar $\phi ^{3}\oplus \phi ^{4}$ theory, is presented. The representation…
A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
In this paper, we study the convergence of Alternating Projection (AP) algorithm for the matrix completion and compressed sensing problems. We also present computational evidence for the excellent performance of the algorithm. Also, in the…
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have…
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak)…
A well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal $a$ on the diagonal and $b$ on the extra diagonals ($a, b\in \mathbb R$). The inverses of such matrices are…
The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast…
The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions required every iteration. In this paper, we study conjugate…
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…
In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…
Geometrical Computation as a new model of computation is the counterpart of Cellular Automata that has Turing computing ability. In this paper we provide an algorithm to simulate Alternating Turing Machine in the context of Signal Machine…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…
Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD)…
A concise analytical formula is developed for the inverse of an invertible 3 x 3 matrix using a telescoping method, and is generalized to larger square matrices. The formula is confirmed using randomly generated matrices in Matlab
Re-Pair is a grammar compression scheme with favorably good compression rates. The computation of Re-Pair comes with the cost of maintaining large frequency tables, which makes it hard to compute Re-Pair on large scale data sets. As a…
As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing…
Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates…