Related papers: ATLAS: Interactive and Educational Linear Algebra …
Recently, reinforcement algorithms discovered new algorithms that really jump-started a wave of excitements and a flourishing of publications. However, there is little on implementations, applications, and, especially, no absolute…
Randomized numerical linear algebra - RandNLA, for short - concerns the use of randomization as a resource to develop improved algorithms for large-scale linear algebra computations. The origins of contemporary RandNLA lay in theoretical…
Continual Learning (CL) methods have traditionally focused on mitigating catastrophic forgetting through gradient-based retraining, an approach ill-suited for deployed agents that must adapt in real time. We introduce our Adaptive Teaching…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Autoformalization, the automatic translation of mathematical content from natural language into machine-verifiable formal languages, has seen significant progress driven by advances in large language models (LLMs). Nonetheless, a primary…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
This paper is to build a primitive framework for a new possible extended system of real mathematical analysis - the Isomorphic Mathematical Analysis System (IMAS). It is based on some new concepts: e.g. isomorphic frame,…
Matrix multiplication $A^t A$ appears as intermediate operation during the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm for the $A^t A$ multiplication. Our algorithm, A$\scriptstyle…
Flipped classroom pedagogy is widely used in undergraduate mathematics to promote active learning, yet it remains unclear whether students experience it in systematically different ways. In this study, we analyze student perceptions from an…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…
Analyzing non-compilable C/C++ submodules without a resolved build environment remains a critical bottleneck for industrial software evolution. Traditional static analysis tools often fail in these scenarios due to their reliance on…
Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…
Current deep learning based text classification methods are limited by their ability to achieve fast learning and generalization when the data is scarce. We address this problem by integrating a meta-learning procedure that uses the…
Although well-trained deep neural networks have shown remarkable performance on numerous tasks, they rapidly forget what they have learned as soon as they begin to learn with additional data with the previous data stop being provided. In…
We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…