Search results for " Multiplication"
showing 10 items of 49 documents
Versatile Direct and Transpose Matrix Multiplication with Chained Operations: An Optimized Architecture Using Circulant Matrices
2016
With growing demands in real-time control, classification or prediction, algorithms become more complex while low power and small size devices are required. Matrix multiplication (direct or transpose) is common for such computation algorithms. In numerous algorithms, it is also required to perform matrix multiplication repeatedly, where the result of a multiplication is further multiplied again. This work describes a versatile computation procedure and architecture: one of the matrices is stored in internal memory in its circulant form, then, a sequence of direct or transpose multiplications can be performed without timing penalty. The architecture proposes a RAM-ALU block for each matrix c…
Reverse-Safe Text Indexing
2021
We introduce the notion of reverse-safe data structures. These are data structures that prevent the reconstruction of the data they encode (i.e., they cannot be easily reversed). A data structure D is called z - reverse-safe when there exist at least z datasets with the same set of answers as the ones stored by D . The main challenge is to ensure that D stores as many answers to useful queries as possible, is constructed efficiently, and has size close to the size of the original dataset it encodes. Given a text of length n and an integer z , we propose an algorithm that constructs a z -reverse-safe data structure ( z -RSDS) that has size O(n) and answers decision and counting pattern matc…
The periods of the generalized Jacobian of a complex elliptic curve
2015
Abstract We show that the toroidal Lie group G = ℂ2/Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian JL of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C fulfilling M − N = [℘ (τ͂) : ℘´(τ͂) : 1] ∈ C. This follows from an apparently new relation between the Weierstrass sigma and elliptic functions.
Quotients of Fermat curves and a Hecke character
2005
AbstractWe explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex multiplication, we verify that both methods give the same result.
A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
2013
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed.
Micropropagation ofAgeratum houstonianumby nodal segments
2017
Ageratum houstonianum is a bedding and flowering potted plant originated from Central America which is generally propagate by seed. In this report a preliminary in vitro technique for propagation of A. houstonianum was investigated. In vitro germinated seeds were used to establish aseptic shoot cultures of several clones. Seedling stem segments bearing 3-4 nodes were placed on Murashige and Skoog (MS) basal medium plus 20 g L-1 sucrose, 8.0 g L-1 Agar to induce axillary shoot development. Axillary shoots were subcultured into the same medium and nodal segments were sectioned and subcultured to increase the stock of shoot cultures. Shoot cultures of the selected clone AG14 were used to accom…
Inductive synthesis of term rewriting systems
2005
Fast algorithm for inductive synthesis of term rewriting systems is described and proved to be correct. It is implemented and successfully applied for inductive synthesis of different algorithms, including the binary multiplication. The algorithm proposed supports automatic learning process and can be used for designing and implementation of ADT.
LightSpMV: Faster CSR-based sparse matrix-vector multiplication on CUDA-enabled GPUs
2015
Compressed sparse row (CSR) is a frequently used format for sparse matrix storage. However, the state-of-the-art CSR-based sparse matrix-vector multiplication (SpMV) implementations on CUDA-enabled GPUs do not exhibit very high efficiency. This has motivated the development of some alternative storage formats for GPU computing. Unfortunately, these alternatives are incompatible with most CPU-centric programs and require dynamic conversion from CSR at runtime, thus incurring significant computational and storage overheads. We present LightSpMV, a novel CUDA-compatible SpMV algorithm using the standard CSR format, which achieves high speed by benefiting from the fine-grained dynamic distribut…
On minimal ∗-identities of matrices∗
1995
Let Mn (F) be the algebra of n×n matrices (n≥2) over a field F of characteristic different from 2 and let ∗ be an involution in Mn (F) In case ∗ is the transpose involution, we construct a multilinear ∗ polynomial identify of Mn (F) of degree 2n−1, P 2n−1(k 1, s 2, … s 2n−1) in one skew variable and the remaining symmetric variables of minimal degree among all ∗-polynomial identities of this type. We also prove that any other multilinear ∗-polynomial identity of Mn (F) of this type of degree 2n−1 is a scalar multiple of P2n−1 . In case ∗ is the symplectic involution in Mn (F), we construct a ∗-polynomial identity of Mn (F) of degree 2n−1 in skew variables T2n−1 (k 1,…,k 2n−1) and we prove t…
Fast Approximated Discriminative Common Vectors Using Rank-One SVD Updates
2013
An efficient incremental approach to the discriminative common vector (DCV) method for dimensionality reduction and classification is presented. The proposal consists of a rank-one update along with an adaptive restriction on the rank of the null space which leads to an approximate but convenient solution. The algorithm can be implemented very efficiently in terms of matrix operations and space complexity, which enables its use in large-scale dynamic application domains. Deep comparative experimentation using publicly available high dimensional image datasets has been carried out in order to properly assess the proposed algorithm against several recent incremental formulations.