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How fast can we compute products?

V. Kislenkov, V. Mitrofanov, E. Zima
1999 Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99  
III this paper we consider the problem of fast computation of n-ary products, for large n, over arbitrary precision integer or ra.tional number domains.  ...  The combinat.ion of loop unrolling, chains of recurrences techniques and analogs of binary powering allows us to obt.ain order-of-magnitude speed improvements for such computations.  ...  III this paper we would like to address a related problem and t,ry to answer the question "how fast we can compute n-ary products for large n?"  ... 
doi:10.1145/309831.309868 dblp:conf/issac/KislenkovMZ99 fatcat:sgqao4xjp5apfo4dhl4n3d27ya

How Fast Can We Multiply Large Integers on an Actual Computer? [article]

Martin Fürer
2014 arXiv   pre-print
We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers.  ...  The Turing machine is more useful here, but fails to take into account the multiplication instruction for short integers, which is available on physical computing devices.  ...  But it does not have the practical advantage of real computers, that can do operations like additions of reasonable numbers almost as fast as a bit operation.  ... 
arXiv:1402.1811v1 fatcat:73lp23v6enevrfnyj52iy6jj5y

S-box Pipelining Using Genetic Algorithms for High-Throughput AES Implementations: How Fast Can We Go? [chapter]

Lejla Batina, Domagoj Jakobovic, Nele Mentens, Stjepan Picek, Antonio de la Piedra, Dominik Sisejkovic
2014 Lecture Notes in Computer Science  
In this manuscript, we explore how Genetic Algorithms (GAs) can be used for pipelining the AES substitution box based on composite field arithmetic.  ...  Implementations of cryptography are of constant interest for companies making security products.  ...  We can either perform the subfield operations directly in GF (2 4 ) or we can perform computations in the tower field GF (((2 2 ) 2 ) 2 ), i.e. working in all subfields and using the fact that inversion  ... 
doi:10.1007/978-3-319-13039-2_19 fatcat:wdqk3a4cmzhgvhp2hy3spmagbm

Products & Materials

1996 Science  
If you are not satisfied with any Epicentre product, we will refund your money.  ...  So, if you're more interested in how it works than how it looks, choose Vibratome.Function is beauty.  ...  Products & Materials  ... 
doi:10.1126/science.273.5281.1571 fatcat:5ba3y7lexfdrrdzhpearwr7kfi

Product modelling and model based product realisation [chapter]

T. Kjellberg
1999 IFIP Advances in Information and Communication Technology  
Product and production models are analysed taking into account human and computer based information processing and intelligence.  ...  A vision of the future production methods and systems is given in this paper. The basic idea is a model based perspective to future product realisation.  ...  How can we characterise a model? How can we validate a model? How can we use a model for different purposes?  ... 
doi:10.1007/978-0-387-35357-9_19 fatcat:dc7upvcv3zg4ta67lat5gijjoa

Information technology and product policy: 'Smart' products

Anirudh Dhebar
1996 European Management Journal  
While these information-technology (IT) applications can-and do-affect a firm's products, the impact usually is indirect.T  ...  benefit-enhancing attributes that can be designed into a product and make it easier and cheaper to change, add, or drop a growing set of attributes.  ...  But the incremental benefits are often uncertain and distant (it may take some time before we can figure out how best to benefit from some IT-based product innovation-and we may 13be disappointed), the  ... 
doi:10.1016/0263-2373(96)00041-2 fatcat:d4rc7uirafae3dcfq7sn2xkdfi

New Products

E. de Lara, K. Farkas
2006 IEEE pervasive computing  
Using DriveSync, vehicle owners can obtain detailed reports of where the vehicle has been, how far it was driven, and how fast.  ...  This product is similar to uLocate Communications' family-finder service, which we reported on in the April-June 2005 issue.  ... 
doi:10.1109/mprv.2006.36 fatcat:2c2bhjvb3zdrtkophrkevtupoq

The ubiquitous Kronecker product

Charles F.Van Loan
2000 Journal of Computational and Applied Mathematics  
The Kronecker product has a rich and very pleasing algebra that supports a wide range of fast, elegant, and practical algorithms.  ...  Second, sparse factorizations and Kronecker products are proving to be a very e ective way to look at fast linear transforms.  ...  We can solve a linear system Ax = b fast if A is a Kronecker product. But fast solutions seem problematical for (4).  ... 
doi:10.1016/s0377-0427(00)00393-9 fatcat:yl6znyoyl5gn3m7iisqtnwg3fu

Mobile product recognition

Sam S. Tsai, David Chen, Vijay Chandrasekhar, Gabriel Takacs, Ngai-Man Cheung, Ramakrishna Vedantham, Radek Grzeszczuk, Bernd Girod
2010 Proceedings of the international conference on Multimedia - MM '10  
We present a mobile product recognition system for the camera-phone. By snapping a picture of a product with a camera-phone, the user can retrieve online information of the product.  ...  We use inverted index compression and fast geometric re-ranking on our database to provide a low delay image recognition response for large scale databases.  ...  We show that by using our approach, we can reduce the total response time of mobile product recognition and provide an interactive experience to the user.  ... 
doi:10.1145/1873951.1874293 dblp:conf/mm/TsaiCCTCVGG10 fatcat:r77uxiattbci7pyhv4tcrcrdfy

Product News

1983 Journal of Automatic Chemistry  
Another important feature is the access to the software we give the customer. Regardless of how thorough we are, we cannot possibly design the software to meet all laboratory needs.  ...  Productivity can be increased at least five times by, for example, fast and accurate peaking on the exact wavelength using CR T display; simultaneous 20-channel dynamic background correction; 20 profiled  ... 
doi:10.1155/s1463924683000541 fatcat:wi25wwqlvfdsplv4yykxmnnh4y

Projective Clustering Product Quantization [article]

Aditya Krishnan, Edo Liberty
2021 arXiv   pre-print
We show that even with comparable running time complexity, in terms of lookup-multiply-adds, projective clustering produces more quantization centers resulting in more accurate dot-product estimates.  ...  This paper suggests the use of projective clustering based product quantization for improving nearest neighbor and max-inner-product vector search (MIPS) algorithms.  ...  how we use the algorithms from Sections 4.1 and 4.2 to compute the index for Q-PCPQ and Q-APCPQ respectively and how the inner-product of the query vector with each point is computed during query time  ... 
arXiv:2112.02179v1 fatcat:yxxazxoxlne7hkn5bsnvw3iwhu

Supporting production planning by production process simulation

Tommi Johtela, Jouni Smed, Mika Johnsson, Risto Lehtinen, Olli Nevalainen
1997 Computer-integrated manufacturing systems  
PCB component printing is used as a case study, but the method can be adapted to other similar environments of generalized flexible flow line.  ...  An interactive production planning system for electronic industry is described.  ...  The processing steps of the product are known in every phase. Similarly, we know for every machine how many processing steps it can do in a time unit on average.  ... 
doi:10.1016/s0951-5240(97)00008-6 fatcat:iud45lv4dvheviy6nu44w43gxa

High-Productivity Software Development with pMatlab

Julie Mullen, Nadya Bliss, Robert Bond, Jeremy Kepner, Hahn Kim, Albert Reuther
2009 Computing in science & engineering (Print)  
We start with a simple serial Matlab code, explore in detail a 1D parallel FFT, and illustrate how it can be extended to multidimensional FFTs.  ...  In this installment of Scientific Programming, we explore the ease of tackling a communication-intensive parallel computing task-namely, the 2D fast Fourier transform (FFT).  ...  The data on other processors needs to be communicated to this processor if required for a subsequent stage of computation or display.  ... 
doi:10.1109/mcse.2009.9 fatcat:ztcabjxoubgoxctkpm46tbrpzy

Fast-Cycle Product Development

Preston G. Smith
1990 Engineering Management Journal  
This article discusses the importance of development speed relative to the product's cost, performance, and development expense, and it suggests ways in which a company can cut development time.  ...  Topics covered include top management involvement; product objectives and complexity; team composition and leadership; communication vehicles, including the product specification; prototyping and testing  ...  The model can be constructed easily on a personal computer by using a spreadsheet program.  ... 
doi:10.1080/10429247.1990.11414568 fatcat:qoy3opiqbnef5jvt24e34ylnxq

Shifted Kronecker Product Systems

Carla D. Moravitz Martin, Charles F. Van Loan
2007 SIAM Journal on Matrix Analysis and Applications  
A fast method for solving a linear system of the form (A (p) ⊗ · · · ⊗ A (1) − λI)x = b is given where each A (i) is an n i -by-n i matrix.  ...  The first step is to convert the problem to triangular form (T (p) ⊗ · · · ⊗ T (1) − λI)y = c by computing the (complex) Schur decompositions of the A (i) .  ...  Perhaps the best example of this is the fast Fourier transform which can be described using the "language" of sparse, matrix factorizations and the Kronecker product.  ... 
doi:10.1137/050631707 fatcat:hdoi4hg4dzdk5dkgxoyqhd7dtq
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