Stat 260 / CS 294 : Randomized Algorithms for Matrices and Data Lecture 5 - 09 / 18 / 2013 Lecture 5 : Matrix Multiplication , Cont . ; and Random Projections
نویسنده
چکیده
Here, we will provide a spectral norm bound for the error of the approximation constructed by the BasicMatrixMultiplication algorithm. Recall that, given as input a m × n matrix A and an n× p matrix B, this algorithm randomly samples c columns of A and the corresponding rows of B to construct a m× c matrix C and a c× p matrix R such that CR ≈ AB, in the sense that some matrix norm ||AB −CR|| is small. The Frobenius norm bound we established before immediately implies a bound for the spectral norm, but in some cases we will need a better bound than can be obtained in this manner. Since, in this semester, we will only need a spectral norm bound for the spectial case that B = AT , that is all that we will consider here.
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