Search · four archives
Search · four archives
12 papers · ranked by Valyu relevance
Daichi Mukunoki, Katsuhisa Ozaki
—To obtain accurate results in numerical computation, high-precision arithmetic is a straightforward approach. However, most processors lack hardware support for floatingpoint formats beyond double precision (FP64). Double-word arithmetic (Dekker 1971) extends precision by using standard floating-point operations to…
Renato J. Cintra, H. M. de Oliveira
Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new…
Shri Prakash Dwivedi
—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 computing GCD and residue operation require at most a factor of log n time more…
Fábio Lourenço Romano
numbers, using floating-point arithmetic Authors: ['Fábio Lourenço Romano'] In this paper, an optimized version of classical Bombelli's algorithm for computing integer square roots is presented. In particular, floating-point arithmetic is used to compute the initial guess of each digit of the root, following similar…
M. Syafiq Johar
We define the regular Euclidean algorithm and the general form which leads to the method of least absolute remainders and also the method of negative remainders. We are going to show that if looked from the perspective of subtraction, the method of least absolute remainders and the regular method have the same number…
Gennadi Malaschonok
Among the set of known algorithms for the determinant computation, there is a subset, which allows us to carry out computations within the commutative ring generated by the coefficients of the system. Recently, interest in these algorithms grew due to computer algebra computations. These algorithms may be used (a) to…
Authors not listed
We present a vector-based method to balance chemical reactions. The algorithm builds candidates in a deterministic way, removes duplicates, and always prints coefficients in the lowest whole-number form. For redox cases, electrons and protons/hydroxide are treated explicitly, so both mass and charge are balanced. We…
Zhihao Lan, WanZhen Liang
The variational quantum eigensolver (VQE) algorithm can simulate the chemical systems such as molecules in the noisy intermediate-scale quantum devices and shows promising applications in quantum chemistry simulations. The accuracy and computational cost of the VQE simulations are determined by the underlying Ansätze.…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
MARCO TODISCO
Determining the distribution of multiple chemical species at equilibrium for a given system is a common problem that must be routinely addressed by scholars. While simple systems consisting of a few species and reactions can be solved manually, most of these problems require the definition and solution of higher-order…
Pavel Pokhilko, Evgeny Epifanovsky, Anna I. Krylov
Using single precision floating point representation reduces the size of data and computation time by a factor of two relative to double precision conventionally used in electronic structure programs. For large-scale calculations, such as those encountered in many-body theories, reduced memory footprint alleviates…
Authors not listed
The SCF part of the HF-SCF method is responsible for finding the ground state as the global minimum of the one-determinant approximation of the electronic energy, which is a 4th order multivariable polynomial of the LCAO coefficients and Lagrange multipliers. In this work we replace this SCF part with algebraic…