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Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable conditions yields a nontrivial factor. In…
We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
In this paper, we describe the randomized QLP (RQLP) algorithm and its enhanced version (ERQLP) for computing the low rank approximation to $A$ of size $m\times n$ efficiently such that $A\approx QLP$, where $L$ is the rank-$k$…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
The Lenstra-Lenstra-Lovasz (LLL) reduction has wide applications in digital communications. It can greatly improve the speed of the sphere decoding (SD) algorithms for solving an integer least squares (ILS) problem and the performance of…
Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is…
We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
The probabilistic threshold query is one of the most common queries in uncertain databases, where a result satisfying the query must be also with probability meeting the threshold requirement. In this paper, we investigate probabilistic…
Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
Simply put, a sparse polynomial is one whose zero coefficients are not explicitly stored. Such objects are ubiquitous in exact computing, and so naturally we would like to have efficient algorithms to handle them. However, with this compact…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
Linear regression in $\ell_p$-norm is a canonical optimization problem that arises in several applications, including sparse recovery, semi-supervised learning, and signal processing. Generic convex optimization algorithms for solving…