We present optimal parallel QR factorization algorithms with reduced communication overhead. QR factorization is widely applied to solve various problems in numerical linear algebra. Our focus is on ...

Add the Householder algorithm, which is generally considered superior to Gram-Schmidt, especially for ill-conditioned matrices. I'm not sure if there is a big difference in arbitrary-precision ...

You have been warned — do not scan here. An “impossible” to detect smartphone threat is now surging, with a new warning that more than 4 million attacks were observed “in the first half of 2025 alone.

One of the main uses of QR decomposition A=QR is in solving the linear least squares problem Ax=b. In order to solve this problem, the only access we need of Q is the ability to apply it (or its ...

Dr. James McCaffrey from Microsoft Research presents a complete end-to-end demonstration of computing a matrix inverse using the Newton iteration algorithm. Compared to other algorithms, Newton ...

Dozens of machine learning algorithms require computing the inverse of a matrix. Computing a matrix inverse is conceptually easy, but implementation is one of the most difficult tasks in numerical ...

Posts from this topic will be added to your daily email digest and your homepage feed. You don’t need an app for this —your phone can do it already. You don’t need an app for this —your phone can do ...

The change will roll out in the coming months and help reduce fraud and spam while improving security. The change will roll out in the coming months and help reduce fraud and spam while improving ...

Google will soon ditch SMS codes for two-factor authentication for Gmail accounts. QR codes will be used instead of SMS codes. This change will reduce the impact of rampant, global SMS abuse. Update, ...