scholarly journals Does a given vector–matrix pair correspond to a PH distribution?

2014 ◽  
Vol 81 ◽  
pp. 40-51 ◽  
Author(s):  
Philipp Reinecke ◽  
Miklós Telek
1989 ◽  
Author(s):  
Ajit Agrawal ◽  
Guy E. Blelloch ◽  
Robert L. Krawitz ◽  
Cynthia A. Phillips
Keyword(s):  

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].


Author(s):  
Dennis R. Bukenberger ◽  
Hendrik P. A. Lensch

Abstract We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities. For objects given as 3D triangle meshes, the method is analytically accurate and at the same time faster than any established approximation method. Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation. The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh. Involved integrals are formulated in closed form and can be evaluated by simple, easily parallelized, vector-matrix multiplications. The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia. In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve $$L_{2|\infty }$$ L 2 | ∞ Lloyd relaxations by exact integration of the Chebyshev norm. In the context of additive manufacturing research, objects of varying density are a prominent topic. However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects. Many existing frameworks will benefit by replacing approximations with fast and exact calculations. Graphic abstract


2007 ◽  
Vol 43 (2-3) ◽  
pp. 425-435 ◽  
Author(s):  
Mitsuhisa Ichiyanagi ◽  
Yohei Sato ◽  
Koichi Hishida
Keyword(s):  

2017 ◽  
Vol 78 ◽  
pp. 60-63 ◽  
Author(s):  
J.A. Ramírez-Cano ◽  
L. Veleva ◽  
R.M. Souto ◽  
B.M. Fernández-Pérez

2010 ◽  
Vol 20 (02) ◽  
pp. 103-121 ◽  
Author(s):  
MOSTAFA I. SOLIMAN ◽  
ABDULMAJID F. Al-JUNAID

Technological advances in IC manufacturing provide us with the capability to integrate more and more functionality into a single chip. Today's modern processors have nearly one billion transistors on a single chip. With the increasing complexity of today's system, the designs have to be modeled at a high-level of abstraction before partitioning into hardware and software components for final implementation. This paper explains in detail the implementation and performance evaluation of a matrix processor called Mat-Core with SystemC (system level modeling language). Mat-Core is a research processor aiming at exploiting the increasingly number of transistors per IC to improve the performance of a wide range of applications. It extends a general-purpose scalar processor with a matrix unit. To hide memory latency, the extended matrix unit is decoupled into two components: address generation and data computation, which communicate through data queues. Like vector architectures, the data computation unit is organized in parallel lanes. However, on parallel lanes, Mat-Core can execute matrix-scalar, matrix-vector, and matrix-matrix instructions in addition to vector-scalar and vector-vector instructions. For controlling the execution of vector/matrix instructions on the matrix core, this paper extends the well known scoreboard technique. Furthermore, the performance of Mat-Core is evaluated on vector and matrix kernels. Our results show that the performance of four lanes Mat-Core with matrix registers of size 4 × 4 or 16 elements each, queues size of 10, start up time of 6 clock cycles, and memory latency of 10 clock cycles is about 0.94, 1.3, 2.3, 1.6, 2.3, and 5.5 FLOPs per clock cycle; achieved on scalar-vector multiplication, SAXPY, Givens, rank-1 update, vector-matrix multiplication, and matrix-matrix multiplication, respectively.


2017 ◽  
Vol 9 (2) ◽  
pp. 74-79 ◽  
Author(s):  
Jin Xiao ◽  
Anderson T Hara ◽  
Dongyeop Kim ◽  
Domenick T Zero ◽  
Hyun Koo ◽  
...  

2005 ◽  
Vol 48 (1) ◽  
pp. 279-285 ◽  
Author(s):  
S. Liu ◽  
V. M. Puri

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