This is the R package to support Computational Methods for
Numerical Analysis with R by James P. Howard, II.
Computational Methods for Numerical Analysis with R is an
overview of traditional numerical analysis topics presented using R.
This guide shows how common functions from linear algebra,
interpolation, numerical integration, optimization, and differential
equations can be implemented in pure R code. Every algorithm described
is given with a complete function implementation in R, along with
examples to demonstrate the function and its use.
Computational Methods for Numerical Analysis with R with R
is intended for those who already know R, but are interested in learning
more about how the underlying algorithms work. As such, it is suitable
for statisticians, economists, and engineers, and others with a
computational and numerical background.
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)
