Related papers: The recursive adaptive quadrature in MS Fortran-77
We study Boolean functions of an arbitrary number of input variables that can be realized by simple iterative constructions based on constant-size primitives. This restricted type of construction needs little global coordination or control…
Comparative analysis of adaptive immune repertoires at population scale is hampered by two practical bottlenecks: the near-quadratic cost of pairwise affinity evaluations and dataset imbalances that obscure clinically important minority…
We introduce a new type of quadrature, known as approximate Gaussian quadrature (AGQ) rules using {\epsilon}-quasiorthogonality, for the approximation of integrals of the form \int f(x)d \alpha(x). The measure {\alpha}(\cdot) can be…
We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…
A mathematical characterization of serially-pruned permutations (SPPs) employed in variable-length permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems…
An important tool in algorithm design is the ability to build algorithms from other algorithms that run as subroutines. In the case of quantum algorithms, a subroutine may be called on a superposition of different inputs, which complicates…
Various methods for the recursive evaluation of scattering amplitudes in quantum field theory and string theory have been put forward during the last couple of years. In these proceedings we describe a geometrical framework, which is…
Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which…
Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often…
Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
A randomised trapezoidal quadrature rule is proposed for continuous functions which enjoys less regularity than commonly required. Indeed, we consider functions in some fractional Sobolev space. Various error bounds for this randomised rule…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…
This paper proposes an adaptive neural-compilation framework to address the problem of efficient program learning. Traditional code optimisation strategies used in compilers are based on applying pre-specified set of transformations that…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…
This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR…
In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms Fast Fourier Transform, Batcher's sorting schemes and prefix sum -exhibit recursive structure. We propose a data structure,…
We provide explicit expressions for quadrature rules on the space of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…