Error-free transformation (EFT) has been recently applied to solve ill-conditioned problems. This transformation can reduce the number of arithmetic operations required compared to multiple precision arithmetic. In this study, we implement double-...
It is well known that Strassen and Winograd algorithms can reduce the computational
costs associated with dense matrix multiplication. We have already shown
that they are also very effective for software-based multiple precision floating-point
ari...
The Strassen algorithm and Winograd's variant accelerate matrix
multiplication by using fewer arithmetic operations than standard matrix
multiplication. Although many papers have been published to accelerate single-
as well as double-precision mat...
BNCpack is a multiple precision numerical computation library built on the functions provided by MPFR/GMP which is currently fastest and the most reliable multiple precision floating-point arithmetic library. It can handle complex arithmetic, basi...
Nowadays, the Jacobian matrix computation is usually based on automatic differentiation(AD). Unless AD can be applied, numerical differentiation is selected. In this case, it generally yields a low precision. However, we can obtain an arbitrary pr...
Kantec method we propose is one of the simulation methods calculating air-flow rate at each air outlet of branch duct system. In this paper, we develop the discrete expressions based on energy equation with loss of energy, and demonstrate the effe...
It is well-known that computing the eigenvalues and eigenvectors of a given matrix A is difficult in case A is not diagonalizable. In this paper, we apply Power methods with Hotelling's, Frazer-Duncan-Collar's and Wielandt's deflations to such mat...
We propose the round-off error estimation using IEEE754 floating-point arithmetic which widely used on various workstations and personal computers. Interval Analysis is one of the standard methods in order to estimatite round-off errors in numeric...
In 1951, Gill proposed a new 4-stage 4th-order explicit Runge-Kutta method, which can diminish the round-off error in the explicit Runge-Kutta process. Moller applied the round-off error correction method to explicit Runge-Kutta process more easil...
International Journal of Numerical Methods and Applications, Vol.7, Issue 2, 2012, Pages 107 - 119 2014年11月
We evaluate the performance of the Krylov subspace method by using highly
efficient multiple precision sparse matrix-vector multiplication (SpMV).
BNCpack is our multiple precision numerical computation library based on
MPFR/GMP, which is one of t...
International Journal of Numerical Methods and Applications, Volume 9, Number 2, 2013, pp.85-108 2013年6月
We propose a practical implementation of high-order fully implicit
Runge-Kutta(IRK) methods in a multiple precision floating-point environment.
Although implementations based on IRK methods in an IEEE754 double precision
environment have been repo...
