Index transformation algorithms in a linear algebra framework
نویسندگان
چکیده
منابع مشابه
Index Transformation Algorithms in a Linear Algebra Framework
We present a linear algebraic formulation for a class of index transformations such as Gray code encoding and decoding, matrix transpose, bit reversal, vector reversal, shuues, and other index or dimension permutations. This formulation uniies, simpliies, and can be used to derive algorithms for hypercube multiprocessors. We show how all the widely known properties of Gray codes and some not so...
متن کاملDesigning Linear Algebra Algorithms by Transformation: Mechanizing the Expert Developer
To implement dense linear algebra algorithms for distributed-memory computers, an expert applies knowledge of the domain, the target architecture, and how to parallelize common operations. This is often a rote process that becomes tedious for a large collection of algorithms. We have developed a way to encode this expert knowledge such that it can be applied by a system to generate mechanically...
متن کاملParallel algorithms in linear algebra
This paper provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues, we consider the problem of parallel solution of a nonsingular linear system by Gaussian elimination with partial pivoting. This problem has come to be regarded...
متن کاملRandomized algorithms in numerical linear algebra
This survey provides an introduction to the use of randomization in the design of fast algorithms for numerical linear algebra. These algorithms typically examine only a subset of the input to solve basic problems approximately, including matrix multiplication, regression and low-rank approximation. The survey describes the key ideas and gives complete proofs of the main results in the field. A...
متن کاملThe Alignment Problem in a Linear Algebra Framework
Two important aspects have to be addressed when automatically parallelizing loop nests for massively parallel distributedmemory computers, namely maximizingparallelism and minimizing communication overhead due to non local data accesses. This paper studies the problem of finding a computation mapping and data distributions that minimize the number of remote data accesses for a given degree of p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Parallel and Distributed Systems
سال: 1994
ISSN: 1045-9219
DOI: 10.1109/71.334903