Randomized numerical linear algebra: Foundations and algorithms

Randomized 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...

Structural Properties Underlying High-Quality Randomized Numerical Linear Algebra Algorithms

In recent years, the amount of data that has been generated and recorded has grown enormously, and data are now seen to be at the heart of modern economic activity, innovation, and growth. See, for example, the report by the McKinsey Global Institute [51], which identifies ways in which Big Data have transformed the modern world, as well as the report by the National Research Council [19], whic...

Numerical Linear Algebra Algorithms and Software

Lectures on Randomized Numerical Linear Algebra

2 Linear Algebra 3 2.1 Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Vector norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Induced matrix norms. . . . . . . . . . . . . . . . . . . . . . . . ....

Linear Algebra: Foundations to Frontiers A Collection of Notes on Numerical Linear Algebra