Computational Methods for Numerical Analysis

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


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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)
      • Quadratic Formula (quadratic, quadratic2)
    • 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
      • Conjugate Gradient (cgmmatrix)
      • 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
      • Quadratic Bezier (qbezier)
      • 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)
    • Adaptive Integrators
      • Recursive Adaptive (adaptint)
      • 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)
      • Gradient Descent (gd, gdls, gradasc, graddsc)
      • 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)
      • Adams-Bashforth (adamsbashforth)
    • Systems of Differential Equations
      • Euler Method (eulersys)
    • Partial Differential Equations
      • Heat Equation, 1D (heat)
      • Wave Equation, 1D (wave)
    • Applications
      • Boundary Value Problems (bvpexample, bvpexample10)

Dependencies

  • testthat
  • roxygen2

Contribution guidelines

For more information

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Reference manual

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install.packages("cmna")

1.0.2 by James Howard, a month ago


https://howardjp.github.io/cmna/


Report a bug at https://github.com/howardjp/cmna/issues


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


Authors: James Howard [aut, cre]


Documentation:   PDF Manual  


BSD_2_clause + file LICENSE license


Suggests testthat


See at CRAN