ABSTRACT: Truncated singular value decomposition (TSVD) and Golub-Kahan diagonalization are two elementary techniques for solving a least squares problem from a linear discrete ill-posed problems. For ...

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

In this video, we explore why Spotify's shuffle feature isn't truly random and operates based on an algorithm. We discuss the reasons behind our preferences for non-random shuffle, the results of an ...

Researchers have successfully used a quantum algorithm to solve a complex century-old mathematical problem long considered impossible for even the most powerful conventional supercomputers. The ...

If you’ve ever shuffled a deck of playing cards, you’ve most likely created a unique deck. That is, you’re probably the only person who has ever arranged the cards in precisely that order. Although ...

Here's the corrected and polished version: Implementation of randomized greedy algorithms for solving the Knapsack Problem and Traveling Salesman Problem in C++. Educational project demonstrating ...

If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle the easiest pieces first. But this kind of sorting has a cost.

One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling discovery about the relationship between time and memory in computing.

The difficulties of algorithmic dynamics in highly nonconvex landscapes are central in several research areas, from hard combinatorial optimization to machine learning. However, it is unclear why and ...