# Computational Methods for Numerical Analysis

Provides the source and examples for James P. Howard, II, "Computational Methods for Numerical Analysis with R," < https://jameshoward.us/cmna>, a book on numerical methods in R.

This is the R package to support Computational Methods for Numerical Analysis with R by James P. Howard, II. This book is scheduled for publication in 2016 and will include a variety of implementations of numerical analysis algorithms in pure R.

## Algorithms included

• Elementary and Example Algorithms
• Polynomial Expansion
• Naive (naivepoly)
• Cached Naive (betterpoly)
• Horner's Method (horner, rhorner)
• Summation
• Naive Summation (naivesum)
• Kahan Summation (kahansum)
• Division
• Naive Division (naivediv)
• Long Division (longdiv)
• Miscellaneous
• Naive Primality tester (isPrime)
• Nth Root (nthroot)
• Samples
• Fibbonaci (fibonacci)
• Wilinson's Polynomial (wilkinson)
• Himmelblau (himmelblau)
• Linear Algebra
• Row/Vector Operations
• Row Replacement (replacerow)
• Scale Row (scalerow)
• Swap Rows (swaprows)
• Norm of a Vector (vecnorm)
• Elementary Functions
• Determinant (detmatrix)
• Matrix Inverse (invmatrix)
• Row-Echelon Form (refmatrix)
• Reduced Row-Echelon Form (rrefmatrix)
• Solve a Matrix, Using Row Reduction (solvematrix)
• Decompositions
• Cholesky Decomposition (choleskymatrix)
• LU Decomposition (lumatrix)
• Iterative Methods
• Gauss Seidel (gaussseidel)
• Jacobi (jacobi)
• Specialty Methods
• Tridiagonal Matrix Solver (tridiagmatrix)
• Interpolation and Extrapolation
• Polynomial Interpolation
• Liner Interpolation (linterp)
• Polynomial Interpolation (polyinterp)
• Splines
• Piecewise Linear (pwiselinterp)
• Cubic Spline (cubicspline)
• Bezier
• Cubic Bezier (cbezier)
• Multidimensional Interpolaters
• Bilinear (bilinear)
• Nearest Neighbor (nn)
• Applications
• Image Resizing (resizeImageNN, resizeImageBL)
• Differentiation
• Finite Differences
• One-Step (findiff)
• More Differentiators (symdiff, rdiff)
• Second Derivative (findiff2)
• Numerical Integration
• Newton-Cotes
• Midpoint Method (midpt)
• Trapezoid Method (trap)
• Simpson's Rule (simp)
• Simpson's 3/8s Rule (simp38)
• Gaussian Integration
• Driver (gaussint)
• Specific forms (gauss.hermite, gauss.laguerre, gauss.legendre)
• Romberg (romberg)
• Monte Carlo
• Monte Carlo Integration, 1D (mcint)
• Monte Carlo Integration, 2D (mcint2)
• Applications
• Shell Method for Revolved Volume (shellmethod)
• Disc Method for Revolved Volume (discmethod)
• Gini Coefficient (giniquintile)
• Root Finding
• Bisection Method (bisection)
• Newton's Method (newton)
• Secant Method (secant)
• Optimization
• Continuous
• Golden Section (goldsectmax, goldsectmin)
• Hill Climbing (hillclimbing)
• Simulated Annealing (sa)
• Discrete
• Traveling Salesperson Problem (tspsa)
• Differential Equations
• Initial Value Problems
• Euler Method (euler)
• Midpoint Method (midptivp)
• Fouth-Order Runge-Kutta (rungekutta4)
• Systems of Differential Equations
• Euler Method (eulersys)
• Partial Differential Equations
• Heat Equation, 1D (heat)
• Wave Equation, 1D (wave)
• Applications
• Boundary Value Problems (bvpexample, bvpexample10)

• testthat
• roxygen2

# Reference manual

install.packages("cmna")

1.0.3 by James Howard, 9 months ago

https://jameshoward.us/cmna

Report a bug at https://github.com/k3jph/cmna-pkg/issues

Browse source code at https://github.com/cran/cmna

Authors: James Howard [aut, cre]

Documentation:   PDF Manual