Generalized matrix inversion is not harder than matrix multiplication
نویسندگان
چکیده
منابع مشابه
Finding a maximum-weight vertex-weighted triangle is not harder than matrix multiplication
We show that a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in timeO(nω+n2+o(1)), where ω is the exponent of fastest matrix multiplication algorithm. By the currently best bound on ω, the running time of our algorithm isO(n2.376). Our algorithm substantially improves the previous time-bounds for this problem recently establish...
متن کاملFinding a Heaviest Vertex-Weighted Triangle Is not Harder than Matrix Multiplication
We show that a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(nω + n2+o(1)), where ω is the exponent of the fastest matrix multiplication algorithm. By the currently best bound on ω, the running time of our algorithm is O(n2.376). Our algorithm substantially improves the previous time-bounds for this problem, and its a...
متن کاملLectures 1 and 2 Matrix Multiplication and Matrix Inversion 1 Prior Work on Matrix Multiplication
There has been much effort to improve the runtime of matrix multiplication. The trivial algorithm multiplies n×n matrices in O(n) time. Strassen (’69) surprised everyone by giving an O(n) time algorithm. This began a long line of improvements until in 1986, Coppersmith and Winograd achieved O(n). After 24 years of no progress, in 2010 Andrew Stothers, a graduate student in Edinburgh, improved t...
متن کاملFast matrix multiplication is stable
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63–72]. As a consequence of our analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also s...
متن کاملTriangular Factorization and Inversion by Fast Matrix Multiplication
The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of ordern in <Cxnlos'7 operations, and, hence, the inverse of any nonsingular matrix in <Cürtlog'7 operations.
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: Journal of Computational and Applied Mathematics
سال: 2009
ISSN: 0377-0427
DOI: 10.1016/j.cam.2008.11.012