"double precision arithmetic" is correct and usable in written English.
It is used to refer to a type of calculation and processing in computers that uses a large number of digits so that the answer is more accurate. For example, "The new processor offers double precision arithmetic for complex calculations."
All computations were carried out using double precision arithmetic.
This is a numerical problem because double precision arithmetic is not associative.
To verify computation results of double precision arithmetic, a high precision arithmetic environment is needed.
First experiments with our C++ implementation, based on double precision arithmetic, demonstrate the adaptability of the algorithm.
In recent computers, it is not difficult to employ not only single or double precision arithmetic but also arbitrary-precision arithmetic or symbolic computing.
The proposed GPU kernels achieve performance speedups vs. CUBLAS of up to 6× for the factorization, and 14× for the inversion, using double precision arithmetic on a Pascal P100 GPU.
It supports algorithms including filtering, auto/cross correlations, transforms, and double-precision arithmetic operations.
Thus, the qd formula serving for constructing a tridiagonal matrix is not so worth in single-precision or double-precision arithmetic.
A popular integrator to perform this task is the fourth-order Hermite predictor-corrector scheme (Makino and Aarseth 1992), using double-precision arithmetic.
The use of double-precision arithmetic can effectively avoid this problem (Fig. 6b); however, it leads to a considerable increase in the memory usage and computation time.
The qd formula, strictly speaking the differential form of it, for computing tridiagonal eigenvalues acts with high relative accuracy in single-precision or double-precision arithmetic [7], while, actually, that serving for constructing a tridiagonal matrix gives rise to no small errors.
