Journal Article10.1109/ASSP.1989.28064
Fast algorithms for complex matrix multiplication using surrogates
F.T. Connolly,Andrew E. Yagle +1 more
162
TL;DR: The 2*2 case of the algorithm can be adapted to computing Givens rotations, resulting in a 17% savings in real matrix multiplications.
read more
Abstract: Novel fast algorithms for multiplying square complex matrices are presented. The algorithms are based on concepts from fast methods of complex multiplication in which a surrogate is used for the square root of minus one. Previous methods imposed the structure of a finite ring or field on the problem. The novel algorithms also use a surrogate, but do not require the imposed structure and its inherent rounding. The number of real matrix multiplications required can be reduced from four to two for even dimension, and to 2+1/N/sup 2/ for odd dimension N. The disadvantage of the algorithms is the imposition of a requirement on the structure of one of the two complex matrices being multiplied. The 2*2 case of the algorithm can be adapted to computing Givens rotations, resulting in a 17% savings in real matrix multiplications. >
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Patent
Intelligent Automated Assistant
Thomas R. Gruber,Adam Cheyer,Dag Kittlaus,Didier Rene Guzzoni,Christopher Dean Brigham,Richard Donald Giuli,Marcello Bastea-Forte,Harry J. Saddler +7 more
- 11 Jan 2011
TL;DR: In this article, an intelligent automated assistant system engages with the user in an integrated, conversational manner using natural language dialog, and invokes external services when appropriate to obtain information or perform various actions.
1.4K
Patent
Automated Response to and Sensing of User Activity in Portable Devices
Brian Q. Huppi,Anthony M. Fadell,Derek Boyd Barrentine,Daniel Freeman +3 more
- 19 Oct 2007
TL;DR: In this paper, various methods and devices described herein relate to devices which, in at least certain embodiments, may include one or more sensors for providing data relating to user activity and at least one processor for causing the device to respond based on the user activity which was determined, at least in part, through the sensors.
844
Patent
Using context information to facilitate processing of commands in a virtual assistant
Thomas R. Gruber,Christopher Dean Brigham,Daniel S. Keen,Gregory Novick,Phipps Benjamin S +4 more
- 28 Sep 2012
TL;DR: In this article, a virtual assistant uses context information to supplement natural language or gestural input from a user, which helps to clarify the user's intent and reduce the number of candidate interpretations of user's input, and reduces the need for the user to provide excessive clarification input.
593
Patent
Method and apparatus for building an intelligent automated assistant
Adam Cheyer,Didier Rene Guzzoni +1 more
- 08 Sep 2006
TL;DR: In this paper, a method for building an automated assistant includes interfacing a service-oriented architecture that includes a plurality of remote services to an active ontology, where the active ontologies includes at least one active processing element that models a domain.
389
Patent
Contextual voice commands
Marcel van Os,Gregory Novick,Scott Herz +2 more
- 05 Jun 2009
TL;DR: In this paper, techniques and systems for implementing contextual voice commands are described and a physical input that relates the selected data item to an operation in a second context is received, and the operation is performed on the input data item in the second context.
385
References
Complex digital signal processing using quadratic residue number systems
TL;DR: The MQRNS is defined, and residue-to-binary conversion techniques in both the QRNS and MqRNS are presented, and hard-ware implementations of multiplication intensive, complex nonrecursive, and recursive digital filters are presented.