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Thursday, July 3, 2008

XNUMBERS 5.6 - Multi Precision Floating Point Computing and Numerical Methods for EXCELâ

Xnumbers is an Excel addin (xla) that performs multi-precision floating point arithmetic from 1 up to 250 significant digits. It is compatible with Excel XP and consists of a set of more than 270 functions/macros for arithmetic, complex , trigonometric, logarithm, exponential calculus. Linear Algebra: System resolution with Gauss-Jordan algorithm (also in a didactic step-by-step method). Gauss-Seidel iterative method. Matrix operations. Determinant. Matrix Inversion. Characteristic Polynomial with Newton-Girard formulas. Crout's algorithm for LU decomposition. Similarity Transform. Matrix power.
Polynomials: symbolic computation to add, multiply, divide polynomials. Derivatives of polynomials. Interpolation with Newton formula. Rootfinder algorithms: Jenkins-Traub, Durand-Kerner-Aberth, Newton Generalized, Laguerre, Siljak, Ruffini. Orthogonal polynomials. Numbers Theory: MCD, MCM, factorization, prime number, fraction reduction, modular power, Diophantine equation, Brouncker-Pell Equation, Integer relation with PSLQ algorithm. Statistic: Mean, Variance, Multivariable Linear Regression, LRE, Probability distributions. Integration : Double Exponetial, Romberg , 2D Romberg, Complex integration, Newton-Cotes, Filon, FFT, DFT, 2D-FFT, Infinite integral. Numerical Series evaluation, real and complex serie. Special function: high precision 64b Bessel, Gamma, Gammaln, Digamma, Incomplete Gamma, Fresnel, integral sine-cosine, exponential integral, error function, Beta, Incomplete Beta, Fibonacci, Airy functions, Elliptic integrals. Interpolation : polynomial, fractional, cubic spline, 2D random interpolation. Derivativse: Gradient vector, Jacobian matrix, Hessian matrix. Diff Equat. Runge-Kutta-4, Adams’s multi-steps, Runge-Kutta-Fehlberg. Optimization on site with Downhill-Simplex (Nelder Maid) algorithm.

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