This library defines basic operation on polynomials, and contains also 3 different roots (zeroes)-finding methods that can handle quite large polynomials (>1000 coefs)
Implemented in ANSI C++ Templates. Handles all real and complex floating point types. Html doc is included.
NTL is a high-performance, portable C++ library providing data structures and algorithms for manipulating signed, arbitrary length integers, and for vectors, matrices, and polynomials over the integers and over finite fields.
The module LSQ is for unconstrained linear least-squares fitting. It is
based upon Applied Statistics algorithm AS 274 (see comments at the start
of the module). A planar-rotation algorithm is used to update the QR-
factorization. This makes it suitable for updating regressions as more
data become available. The module contains a test for singularities which
is simpler and quicker than calculating the singular-value decomposition.
An important feature of the algorithm is that it does not square the condition
number. The matrix X X is not formed. Hence it is suitable for ill-
conditioned problems, such as fitting polynomials.
By taking advantage of the MODULE facility, it has been possible to remove
many of the arguments to routines. Apart from the new function VARPRD,
and a back-substitution routine BKSUB2 which it calls, the routines behave
as in AS 274.
Math.NET開源數(shù)學(xué)庫
C#實現(xiàn)
具體功能:
- A linear algebra package, see MathNet.Numerics.LinearAlgebra.
- A sparse linear algebra package, see MathNet.Numerics.LinearAlgebra.Sparse.
- Non-uniform random generators, see MathNet.Numerics.Generators.
- Distribution fonctions, see MathNet.Numerics.Distributions.
- Statistical accumulator, see MathNet.Numerics.Statistics.
- Fourier transformations, see MathNet.Numerics.Transformations.
- Miscellaneous utilies (polynomials, rationals, collections).
simulating a convolutional encoder
allows the user to input a source code to be encoded and also input the values of the generator polynomials. It outputs the encoded data bits, where 1/n is the code rate
多項式擬合的MATLAB工具。只要具有以下幾個函數(shù)
POLYFITN - A general n-dimensional polynomial fitting tool
POLYVALN - An evaluation tool for polynomials produced by polyfitn
POLYN2SYMPOLY - A conversion tool to generate a sympoly from the results of polyfitn
POLYN2SYM - A conversion tool to generate a symbolic toolbox object from the results of polyfitn
密碼學(xué)界牛人Victor Shoup用C++編寫數(shù)論類庫。
NTL is a high-performance, portable C++ library providing data structures and algorithms for arbitrary length integers for vectors, matrices, and polynomials over the integers and over finite fields and for arbitrary precision floating point arithmetic.
NTL provides high quality implementations of state-of-the-art algorithms for:
* arbitrary length integer arithmetic and arbitrary precision floating point arithmetic
* polynomial arithmetic over the integers and finite fields including basic arithmetic, polynomial factorization, irreducibility testing, computation of minimal polynomials, traces, norms, and more
* lattice basis reduction, including very robust and fast implementations of Schnorr-Euchner, block Korkin-Zolotarev reduction, and the new Schnorr-Horner pruning heuristic for block Korkin-Zolotarev
* basic linear algebra over the integers, finite fields, and arbitrary precision floating point numbers.
We introduce a sub-cell WENO reconstruction method to evaluate spatial derivatives in the high-order ADER scheme. The basic idea in our reconstruction is to use only r stencils to reconstruct the point-wise values of solutions and spatial derivatives for the 2r-1 th order
ADER scheme in one dimension, while in two dimensions, the dimension-by-dimension sub-cell reconstruction approach for spatial derivatives is employed. Compared with the original ADER scheme of Toro and Titarev (2002) [2] that uses the direct derivatives of reconstructed polynomials for solutions to evaluate spatial derivatives, our method not only reduces greatly the computational costs of the ADER scheme on a given mesh,
but also avoids possible numerical oscillations near discontinuities, as demonstrated by a number of one- and two-dimensional numerical tests. All these tests show that the 5th-order ADER scheme based on our sub-cell reconstruction method achieves the desired accuracy, and is essentially non-oscillatory and computationally cheaper for problems with discontinuities.
