## 9 Citations

### A Two-pronged Progress in Structured Dense Matrix Vector Multiplication

- Mathematics, Computer ScienceSODA
- 2018

This work unifies, generalizes, and simplifies existing state-of-the-art results in structured matrix-vector multiplication, and shows how applications in areas such as multipoint evaluations of multivariate polynomials can be reduced to problems involving low recurrence width matrices.

### LDU factorization

- Computer Science, MathematicsArXiv
- 2020

This work proposes a generalization of the LEU algorithm to the case of a commutative domain and its field of quotients, and decomposes the matrix over the commutatives into a product of three matrices, in which the matrices L and U belong to the commUTative domain, and the elements of the weighted truncated permutation matrix D are the elements inverse to the product of some pair of minors.

### Sparse matrices in computer algebra when using distributed memory: theory and applications: [preprint]

- Computer Science
- 2017

J. Dongarra puts attansion on the several difficult challenges of managing calculations on a cluster with distributed memory for algorithms with sparse matrices, and considers the class of block-recursive matrix algorithms, the most famous of them are standard and Strassen's block matrix multiplication, Schur andStrassen’s block-matrix inversion.

### Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic

- Computer Science, MathematicsSIAM J. Matrix Anal. Appl.
- 2019

A new BLR factorization algorithm is devised that, by recasting the operations so as to work on intermediate matrices of larger size, can exploit more efficiently fast matrix arithmetic.

### Exploiting Fast Matrix Arithmetic in Block Low-Rank Factorizations

- Computer Science, Mathematics
- 2019

A new BLR factorization algorithm is devised that, by recasting the operations so as to work on intermediate matrices of larger size, can exploit more efficiently fast matrix arithmetic.

### Recursive Matrix Algorithms in Commutative Domain for Cluster with Distributed Memory

- Computer Science2018 Ivannikov Memorial Workshop (IVMEM)
- 2018

This class of algorithms allows to obtain efficient parallel programs on clusters with distributed memory and to demonstrate a scalability of these programs is measured.

### Calculation Managing on a Cluster with Distributed Memory

- Computer Science
- 2017

A scheme with multidispatching for management of such parallel computing processes for cluster with distributed memory is suggested and the results of experiments at the JSC RAS cluster MVS-10P are demonstrated.

### Recursive Matrix Algorithms, Distributed Dynamic Control, Scaling, Stability

- Computer Science2019 Computer Science and Information Technologies (CSIT)
- 2019

The report is devoted to the concept of creating block-recursive matrix algorithms for computing on a super-computer with distributed memory and dynamic decentralized control.

### Twin-width V: linear minors, modular counting, and matrix multiplication

- Mathematics, Computer ScienceArXiv
- 2022

The notion of parity and linear minors of a matrix, which consists of iteratively replacing consecutive rows or consecutive columns with a linear combination of them is introduced, and an ad hoc algorithm to efficiently multiply two matrices of bounded twin-width is presented.

## References

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- Computer Science, MathematicsISSAC
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This paper shows the connection between the notion of quasiseparability and the rank profile matrix invariant, presented in [Dumas & al. ISSAC'15], and proposes an algorithm computing the quasieparable orders (rL,rU) in time O{n2sω-2} where s=max( rL, rU) and ω the exponent of matrix multiplication.

### Algorithms to solve hierarchically semi-separable systems

- Computer Science, Mathematics
- 2007

A survey of the main results, including a proof for the formulas for LU-factorization that were given in the thesis of Lyon, the derivation of an explicit algorithm for ULV factorization and related Moore-Penrose inversion, a complexity analysis and a short account of the connection between the HSS and the SSS (sequen- tially semi-separable) case are given.

### Fast algorithms for hierarchically semiseparable matrices

- Computer Science, MathematicsNumer. Linear Algebra Appl.
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This paper generalizes the hierarchically semiseparable (HSS) matrix representations and proposes some fast algorithms for HSS matrices that are useful in developing fast‐structured numerical methods for large discretized PDEs, integral equations, eigenvalue problems, etc.

### A bibliography on semiseparable matrices*

- Mathematics
- 2005

Currently there is a growing interest in semiseparable matrices and generalized semiseparable matrices. To gain an appreciation of the historical evolution of this concept, we present in this paper…

### Rank-profile revealing Gaussian elimination and the CUP matrix decomposition

- Computer ScienceJ. Symb. Comput.
- 2013

### A Givens-Weight Representation for Rank Structured Matrices

- Computer Science, MathematicsSIAM J. Matrix Anal. Appl.
- 2007

In this paper we introduce a Givens-weight representation for rank structured matrices, where the rank structure is defined by certain submatrices starting from the bottom left or upper right matrix…

### Fast computation of the rank profile matrix and the generalized Bruhat decomposition

- Computer Science, MathematicsJ. Symb. Comput.
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### Some Fast Algorithms for Sequentially Semiseparable Representations

- Computer ScienceSIAM J. Matrix Anal. Appl.
- 2005

An extended sequentially semiseparable (SSS) representation derived from time-varying system theory is used to capture the low-rank of the off-diagonal blocks of a matrix for the purposes of efficient computations and for sufficient descriptive richness to allow for backward stability in the computations.