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- symbolic matrices; arbitrary precision integer and real arithmetic; facilities for defining new functions and extending...
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- 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 ... interpreted, reference implementation, slow) multiple precision interval arithmetic with error bounds (does the job, slow...
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- 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...
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- Microsoft Research.Z3 supports linear real and integer arithmetic, fixed-size bit-vectors, extensional arrays, uninterpreted...
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- MACHAR software for dynamically determining machine-dependent arithmetic properties...
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- matrices; general unsymmetric matrices; Version for complex arithmetic; Parallel factorization and solve phases (uniprocessor version...
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- free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point ... achieved by using fullwords as the basic arithmetic type, by using fast algorithms, with highly...
- Referenced in 216 articles
- ANSI/IEEE-754 standard for double-precision floating-point arithmetic (53-bit significand). MPFR is free...
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- semi-numerical version, using multi-precision interval arithmetic. We finally show that these critical optimizations...
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- integration of a linear arithmetic decision procedure and the addition of a rather primitive facility...
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- symbols with equality, linear real and integer arithmetic, scalar types, recursive datatypes, tuples, records, extensional...
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- PROFIL is based on BIAS (Basic Interval Arithmetic Subroutines). The developement of BIAS was guided...
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- library of logical theories (integer and real arithmetic, Boolean operations, sets and maps...
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- package provides support for several extended precision arithmetics, including user-defined types. par The authors ... true for integrations that require extended precision arithmetic. The main drawback is that the Taylor...
- Referenced in 116 articles
- Common Lisp. Lisp-Stat extends standard Lisp arithmetic operations to perform element-wise operations...
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- dynamics of the system. PHAVer’s exact arithmetic is robust...
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- which performs basic algebraic operations, such as arithmetic operations, to algebraic objects, e.g., numbers...
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- upon a properly defined and implemented computer arithmetic in the usual spaces of numerical computation...
- Referenced in 99 articles
- accuracy on multiple roots without using multiprecision arithmetic, even if the polynomial coefficients are inexact...
- Referenced in 57 articles
- differentiate functions that are implemented in arithmetic types, such as doubles and intervals ... template types also behave like arithmetic types. This property of the AD-templates enables ... replacing all occurrences of the original arithmetic type with the AD-template version. This transparency...