Related papers: Twofold fast arithmetic
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
Abstraction (in its various forms) is a powerful established technique in model-checking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an…
Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
Algorithms operating on real numbers are implemented as floating-point computations in practice, but floating-point operations introduce roundoff errors that can degrade the accuracy of the result. We propose $\Lambda_{num}$, a functional…
The continuous Frechet distance between two polygonal curves is classically computed by exploring their free space diagram. Recently, Har-Peled, Raichel, and Robson [SoCG'25] proposed a radically different approach: instead of directly…
Finding a good regularization parameter for Tikhonov regularization problems is a though yet often asked question. One approach is to use leave-one-out cross-validation scores to indicate the goodness of fit. This utilizes only the noisy…
Floating-point programs form the foundation of modern science and engineering, providing the essential computational framework for a wide range of applications, such as safety-critical systems, aerospace engineering, and financial analysis.…
Block Floating Point (BFP) can efficiently support quantization for Deep Neural Network (DNN) training by providing a wide dynamic range via a shared exponent across a group of values. In this paper, we propose a Fast First, Accurate Second…
In this paper, we present a domain specific process to assist the verification of observer-based fault detection software. Observer-based fault detection systems, like control systems, yield invariant properties of quadratic types. These…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…
We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…
Many modern solvers and program analyzers rely on non-monotone reasoning (e.g. negation-as-failure, speculative updates, backtracking) for which classical monotone fixed-point methods do not apply. The general problem of finding the fixed…
Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While…
This paper presents convergence acceleration, a method for computing efficiently the limit of numerical sequences as a typical application of streams and higher-order functions.
Zigzag persistence is a powerful extension of the standard persistence which allows deletions of simplices besides insertions. However, computing zigzag persistence usually takes considerably more time than the standard persistence. We…
Fast matching of regular expressions with bounded repetition, aka counting, such as (ab){50,100}, i.e., matching linear in the length of the text and independent of the repetition bounds, has been an open problem for at least two decades.…
Verification of numerical accuracy properties in modern software remains an important and challenging task. This paper describes an original framework combining different solutions for numerical accuracy. First, we extend an existing…