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We study the bit complexity of two related fundamental computational problems in linear algebra and control theory. Our results are: (1) An $\tilde{O}(n^{\omega+3}a+n^4a^2+n^\omega\log(1/\epsilon))$ time algorithm for finding an…
Modern lunar-planetary ephemerides are numerically integrated on the observational timespan of more than 100 years (with the last 20 years having very precise astrometrical data). On such long timespans, not only finite difference…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100:1. Our technique for evolving such extreme mass ratios is based on the moving puncture approach with a new gauge condition and an optimal…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
Multiplication is one of the most important operation in computer arithmetic. Many integer operations such as squaring, division and computing reciprocal require same order of time as multiplication whereas some other operations such as…
Halfspaces or linear threshold functions are widely studied in complexity theory, learning theory and algorithm design. In this work we study the natural problem of constructing pseudorandom generators (PRGs) for halfspaces over the sphere,…
Numerical-relativity simulations offer a unique approach to investigating the dynamics of binary neutron star mergers and provide the most accurate predictions of waveforms in the late inspiral phase. However, the numerical predictions are…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
We describe and study an instantaneous definition of eccentricity to be applied at the initial moment of full numerical simulations of binary black holes. The method consists of evaluating the eccentricity at the moment of maximum…
Numerical relativity (NR) simulations of binary black hole (BBH) systems provide the most accurate gravitational wave predictions, but at a high computational cost -- especially when the black holes have nearly extremal spins (i.e. spins…
We present a new algorithm for refining a real interval containing a single real root: the new method combines characteristics of the classical Bisection algorithm and Newton's Iteration. Our method exhibits quadratic convergence when…
We develop an accurate square-root-free algorithm for constructing real Givens rotations. On processors that support the fused multiply-add operation in hardware, the algorithm is competitive with square-root based algorithms using a…
For an arbitrary strong, spherically symmetric super-horizon curvature perturbation, we present analytical solutions of the Einstein equations in terms of asymptotic expansion over the ratio of the Hubble radius to the length-scale of the…
We present and experimentally implement a real-time protocol for calibrating the frequency of a resonantly driven qubit, achieving exponential scaling in calibration precision with the number of measurements, up to the limit imposed by…
With recent advances in post-Newtonian (PN) theory and numerical relativity (NR) it has become possible to construct inspiral-merger-ringdown waveforms by combining both descriptions into one hybrid signal. While addressing the reliability…
Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the Einstein-Euler system of equations. We report simulations of the inspiral of binary neutron stars in…
Accurate modelling of black hole binaries is critical to achieve the science goals of gravitational-wave detectors. Modelling such configurations relies strongly on calibration to numerical-relativity (NR) simulations. Binaries on…
The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized. Computationnally effective fast and accurate)tools for constructing gravitational wave templates from binary…