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Communication-avoiding Algorithm
Communication-avoiding algorithms minimize movement of data within a memory hierarchy for improving its running-time and energy consumption. These minimize the total of two costs (in terms of time and energy): arithmetic and communication. Communication, in this context refers to moving data, either between levels of memory or between multiple processors over a network. It is much more expensive than arithmetic. Formal theory Two-level memory model A common computational model in analyzing communication-avoiding algorithms is the two-level memory model: * There is one processor and two levels of memory. * Level 1 memory is infinitely large. Level 0 memory ("cache") has size M. * In the beginning, input resides in level 1. In the end, the output resides in level 1. * Processor can only operate on data in cache. * The goal is to minimize data transfers between the two levels of memory. Matrix multiplication Corollary 6.2: More general results for other numerical linear al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memory Hierarchy
In computer architecture, the memory hierarchy separates computer storage into a hierarchy based on response time. Since response time, complexity, and capacity are related, the levels may also be distinguished by their performance and controlling technologies. Memory hierarchy affects performance in computer architectural design, algorithm predictions, and lower level programming constructs involving locality of reference. Designing for high performance requires considering the restrictions of the memory hierarchy, i.e. the size and capabilities of each component. Each of the various components can be viewed as part of a hierarchy of memories in which each member is typically smaller and faster than the next highest member of the hierarchy. To limit waiting by higher levels, a lower level will respond by filling a buffer and then signaling for activating the transfer. There are four major storage levels. * ''Internal''processor registers and cache. * Mainthe system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CPU Cache
A CPU cache is a hardware cache used by the central processing unit (CPU) of a computer to reduce the average cost (time or energy) to access data from the main memory. A cache is a smaller, faster memory, located closer to a processor core, which stores copies of the data from frequently used main memory locations. Most CPUs have a hierarchy of multiple cache levels (L1, L2, often L3, and rarely even L4), with different instruction-specific and data-specific caches at level 1. The cache memory is typically implemented with static random-access memory (SRAM), in modern CPUs by far the largest part of them by chip area, but SRAM is not always used for all levels (of I- or D-cache), or even any level, sometimes some latter or all levels are implemented with eDRAM. Other types of caches exist (that are not counted towards the "cache size" of the most important caches mentioned above), such as the translation lookaside buffer (TLB) which is part of the memory management unit (M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Computing
Parallel computing is a type of computing, computation in which many calculations or Process (computing), processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: Bit-level parallelism, bit-level, Instruction-level parallelism, instruction-level, Data parallelism, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling.S.V. Adve ''et al.'' (November 2008)"Parallel Computing Research at Illinois: The UPCRC Agenda" (PDF). Parallel@Illinois, University of Illinois at Urbana-Champaign. "The main techniques for these performance benefits—increased clock frequency and smarter but increasingly complex architectures—are now hitting the so-called power wall. The computer industry has accepted that future performance inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laura Grigori
Laura Grigori is a French-Romanian applied mathematician and computer scientist known for her research on numerical linear algebra and communication-avoiding algorithms. She is a director of research for the French Institute for Research in Computer Science and Automation (INRIA) in Paris, and heads the "Alpines" scientific computing project jointly affiliated with INRIA and the of Sorbonne University. Education and career Grigori earned her Ph.D. from Henri Poincaré University in 2001. Her dissertation, ''Prédiction de structure et algorithmique parallèle pour la factorisation LU des matrices creuses'', concerned parallel algorithms for LU decomposition of sparse matrices, and was supervised by . After postdoctoral research at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, she became a researcher for INRIA in 2004, and became the head of the Alpines project in 2013. In 2021, she will join the SIAM Council as a Member-at-Large. Recogni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Processing Techniques Office
The Information Processing Techniques Office (IPTO), originally "Command and Control Research",Lyon, Matthew; Hafner, Katie (1999-08-19). ''Where Wizards Stay Up Late: The Origins Of The Internet'' (p. 39). Simon & Schuster. Kindle Edition. was part of the Defense Advanced Research Projects Agency of the United States Department of Defense. Origin According to an ARPA-sponsored history of the organization, IPTO grew from a distinctly unpromising beginning: the Air Force had a large, expensive computer ( AN/FSQ 321A) which was intended as a backup for the SAGE air defense program, but no longer needed; and it also had too few required tasks to maintain the desired staffing level at its main software contractor, the System Development Corporation (SDC). Accordingly, the Under Secretary of Defense for Research and Engineering decided to capitalize on these "sunk costs" and SDC expertise by standing up an ARPA program in Command & Control Research. It was accordingly begun in June 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Defense Advanced Research Projects Agency
The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Advanced Research Projects Agency (ARPA), the agency was created on February 7, 1958, by President Dwight D. Eisenhower in response to the Soviet launching of Sputnik 1 in 1957. By collaborating with academia, industry, and government partners, DARPA formulates and executes research and development projects to expand the frontiers of technology and science, often beyond immediate U.S. military requirements.Dwight D. Eisenhower and Science & Technology, (2008). Dwight D. Eisenhower Memorial CommissionSource The name of the organization first changed from its founding name, ARPA, to DARPA, in March 1972, changing back to ARPA in February 1993, then reverted to DARPA in March 1996. ''The Economist'' has called DARPA "the agency that shaped the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Locality
Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data are usually organized into structures such as tables that provide additional context and meaning, and may themselves be used as data in larger structures. Data may be used as variables in a computational process. Data may represent abstract ideas or concrete measurements. Data are commonly used in scientific research, economics, and virtually every other form of human organizational activity. Examples of data sets include price indices (such as the consumer price index), unemployment rates, literacy rates, and census data. In this context, data represent the raw facts and figures from which useful information can be extracted. Data are collected using techniques ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Fourier Transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by Matrix decomposition, factorizing the DFT matrix into a product of Sparse matrix, sparse (mostly zero) factors. As a result, it manages to reduce the Computational complexity theory, complexity of computing the DFT from O(n^2), which arises if one simply applies the definition of DFT, to O(n \log n), where is the data size. The difference in speed can be enormous, especially for long data sets where may be in the thousands or millions. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cache-oblivious Algorithm
In computing, a cache-oblivious algorithm (or cache-transcendent algorithm) is an algorithm designed to take advantage of a processor cache without having the size of the cache (or the length of the cache lines, etc.) as an explicit parameter. An optimal cache-oblivious algorithm is a cache-oblivious algorithm that uses the cache optimally (in an asymptotic sense, ignoring constant factors). Thus, a cache-oblivious algorithm is designed to perform well, without modification, on multiple machines with different cache sizes, or for a memory hierarchy with different levels of cache having different sizes. Cache-oblivious algorithms are contrasted with explicit '' loop tiling'', which explicitly breaks a problem into blocks that are optimally sized for a given cache. Optimal cache-oblivious algorithms are known for matrix multiplication, matrix transposition, sorting, and several other problems. Some more general algorithms, such as Cooley–Tukey FFT, are optimally cache-oblivio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Multiplication Algorithm Diagram
Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the material in between a eukaryotic organism's cells * Matrix (chemical analysis), the non-analyte components of a sample * Matrix (geology), the fine-grained material in which larger objects are embedded * Matrix (composite), the constituent of a composite material * Hair matrix, produces hair * Nail matrix, part of the nail in anatomy Technology * Matrix (mass spectrometry), a compound that promotes the formation of ions * Matrix (numismatics), a tool used in coin manufacturing * Matrix (printing), a mould for casting letters * Matrix (protocol), an open standard for real-time communication * Matrix (record production), or master, a disc used in the production of phonograph records ** Matrix number, of a gramophone record * Diode matrix, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communication-avoiding Algorithm
Communication-avoiding algorithms minimize movement of data within a memory hierarchy for improving its running-time and energy consumption. These minimize the total of two costs (in terms of time and energy): arithmetic and communication. Communication, in this context refers to moving data, either between levels of memory or between multiple processors over a network. It is much more expensive than arithmetic. Formal theory Two-level memory model A common computational model in analyzing communication-avoiding algorithms is the two-level memory model: * There is one processor and two levels of memory. * Level 1 memory is infinitely large. Level 0 memory ("cache") has size M. * In the beginning, input resides in level 1. In the end, the output resides in level 1. * Processor can only operate on data in cache. * The goal is to minimize data transfers between the two levels of memory. Matrix multiplication Corollary 6.2: More general results for other numerical linear al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
