- Referenced in 426 articles
- univariate polynomial zeros (simple and clusters) interval arithmetic for real and complex data including vectors ... matrices (very fast) interval arithmetic for real and complex sparse matrices (very fast) automatic differentiation ... simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very ... interpreted, reference implementation, slow) multiple precision interval arithmetic with error bounds (does the job, slow...
- Referenced in 304 articles
- monograph gives a survey of interval arithmetic based methods for solving systems of equations ... almost unavoidable part of optimization. The interval arithmetic philosophy of selfvalidation is followed ... software and library packages for interval arithmetic and the solvers for the above mentioned problems ... first chapter (69 pages) introduces interval arithmetic, solving linear interval equations, automatic differentiation and code...
- Referenced in 213 articles
- semi-numerical version, using multi-precision interval arithmetic. We finally show that these critical optimizations...
- Referenced in 133 articles
- PROFIL is based on BIAS (Basic Interval Arithmetic Subroutines). The developement of BIAS was guided ... give such an interface for interval operations with the objective: very efficient...
- Referenced in 40 articles
- Motivations for an arbitrary precision interval arithmetic and the MPFI library. This paper justifies ... arbitrary precision interval arithmetic is needed. To provide accurate results, interval computations require small input ... comparison with a fixed-precision interval arithmetic, on a specific problem, is presented. It shows...
- Referenced in 49 articles
- with rounding control, interval and complex interval arithmetic, accurate vector/matrix arithmetic, an enlarged...
- Referenced in 50 articles
- defined by analytical expressions involving usual arithmetic operations and transcendental elementary functions. Rigourousness: Realpaver covers ... certainty. Solving methods: Realpaver implements correctly rounded interval-based computations in a branch-and-bound ... benchmarks are also provided. Interval arithmetic is supported by gaol...
- Referenced in 29 articles
- readily available, portable, exhaustively documented interval arithmetic library, written in standard Fortran 77. Its underlying ... philosophy is to provide a standard for interval operations ... efficiently transporting programs involving interval arithmetic. The model is the BLAS package, for basic linear ... library is composed of elementary interval arithmetic routines, standard function routines for interval data...
- Referenced in 40 articles
- Python library for arbitrary-precision floating-point arithmetic. It implements the standard functions from Python ... numerical differentiation, integration, root-finding, and interval arithmetic. It supports unlimited exponent sizes, has full...
Boost Interval Arithmetic
- Referenced in 15 articles
- design of the Boost interval arithmetic library. We present the design of the Boost interval ... arithmetic library, a C++ library designed to handle mathematical intervals efficiently and in a generic ... have a mathematically correct implementation of interval arithmetic. Various implementations exist with diverse semantics ... specialized libraries available for interval arithmetic, without any loss of performance nor sacrificing the ease...
- Referenced in 24 articles
- from a classical method that uses interval arithmetic to check whether trajectories can move over...
- Referenced in 10 articles
- Algorithm 763: INTERVAL - ARITHMETIC: A Fortran 90 module for an interval data type Interval arithmetic ... certain bounds. In addition to rigor, interval arithmetic also provides a simple and sometimes sharp ... other tasks. Convenient use of interval arithmetic requires an interval data type in the programming ... commercial. The Fortran 90 module INTERVAL - ARITHMETIC provides a portable interval data type in Fortran...
- Referenced in 13 articles
- Gaol is a C++ library for interval arithmetic. It is supposed to be a fast ... library for anyone interested in assessing interval arithmetic merits or using it on a regular...
- Referenced in 55 articles
- that are implemented in arithmetic types, such as doubles and intervals. One of the major ... template types also behave like arithmetic types. This property of the AD-templates enables...
- Referenced in 9 articles
- experimental interval arithmetic package in Maple. We describe an experimental arbitrary-precision interval arithmetic package ... those of the proposed Basic Interval Arithmetic Subroutine (BIAS) library. We give here an overview...
- Referenced in 14 articles
- this author) to support variable precision interval arithmetic. It appears to be the oldest...
- Referenced in 9 articles
- this open source software, describes how interval arithmetic help to implement new transmission elements ... enhance already existing modeling software with interval arithmetic concepts...
- Referenced in 12 articles
- into account. It is based on interval arithmetic and affine arithmetic. The main feature...
- Referenced in 8 articles
- background theories, which are various interval arithmetics. Main features are: raSAT applies raSAT loop, which ... holds, raSAT loop refines bounded quantification by interval decompositions. raSAT is based on an interval ... similar to HySAT. raSAT prepares various interval arithmetics as over-approximation theories, which are mostly...
- Referenced in 5 articles
- development of hardware support for interval arithmetic. This paper describes modifications made ... Fortran compiler to provide support for interval arithmetic. These modifications are based on a recently ... proposed Fortran 77 interval arithmetic specification, which provides a standard for supporting interval arithmetic...