Computational Methods for Numerical Analysis with R
Book details, ISBNs, DOI, chapter structure, purchase links, and the role of CMNA as a computational treatment of numerical analysis.
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Find the thing you actually came for.
Search methods, R functions, laboratories, teaching material, and the Numerical Zoo. This is deliberately a site index, not a general numerical analysis search engine.
CMNA Laboratory
Interactive numerical-analysis laboratories powered by real R in the browser, with playback, source inspection, export, sharing, and Workbench handoff.
CMNA software
The cmna R package, companion source code, package DOI, GitHub repository, and Emacs support.
Teaching with CMNA
Course maps, chapter guidance, laboratory notes, Break It assignments, adoption material, and prediction worksheets.
Fourteen weeks with CMNA
A complete semester course map pairing chapters, classroom demonstrations, laboratories, and assignment seeds.
Chapter guide
Learning objectives, representative functions, laboratory crosswalks, and misconceptions worth provoking across all seven chapters.
Teaching with the laboratories
Prediction questions, public parameter changes, and follow-up prompts for the CMNA browser laboratories.
Break It
Failure-driven numerical-analysis exercises built around cancellation, instability, bad starting values, conditioning, and convergence assumptions.
Adopting CMNA
Prerequisites, course roles, software expectations, sample syllabus language, and assessment guidance.
Citing CMNA
Book, package, and website citations with downloadable BibTeX and RIS files.
Updates and errata
Corrections, software changes, teaching additions, and continuing project updates around the 2017 book.
R Workbench
An unrestricted browser-side R session using webR with CMNA functions loaded.
Method finder
A guided decision tree for moving from a computational problem to suitable CMNA methods.
Naive polynomial evaluation
Error and elementary computation. CMNA functions: naivepoly.
Cached polynomial evaluation
Error and elementary computation. CMNA functions: betterpoly.
Horner's method
Error and elementary computation. CMNA functions: horner, rhorner.
Naive summation
Error and elementary computation. CMNA functions: naivesum.
Kahan summation
Error and elementary computation. CMNA functions: kahansum.
Naive division
Error and elementary computation. CMNA functions: naivediv.
Long division
Error and elementary computation. CMNA functions: longdiv.
Primality test
Error and elementary computation. CMNA functions: isPrime.
Nth root
Error and elementary computation. CMNA functions: nthroot.
Quadratic formula
Error and elementary computation. CMNA functions: quadratic, quadratic2.
Fibonacci sequence
Error and elementary computation. CMNA functions: fibonacci.
Wilkinson's polynomial
Error and elementary computation. CMNA functions: wilkinson.
Himmelblau function
Error and elementary computation. CMNA functions: himmelblau.
Row replacement
Linear algebra. CMNA functions: replacerow.
Row scaling
Linear algebra. CMNA functions: scalerow.
Row swapping
Linear algebra. CMNA functions: swaprows.
Vector norm
Linear algebra. CMNA functions: vecnorm.
Determinant
Linear algebra. CMNA functions: detmatrix.
Matrix inverse
Linear algebra. CMNA functions: invmatrix.
Row-echelon form
Linear algebra. CMNA functions: refmatrix.
Reduced row-echelon form
Linear algebra. CMNA functions: rrefmatrix.
Solve by row reduction
Linear algebra. CMNA functions: solvematrix.
Cholesky decomposition
Linear algebra. CMNA functions: choleskymatrix.
LU decomposition
Linear algebra. CMNA functions: lumatrix.
Conjugate gradient
Linear algebra. CMNA functions: cgmmatrix.
Gauss-Seidel iteration
Linear algebra. CMNA functions: gaussseidel.
Jacobi iteration
Linear algebra. CMNA functions: jacobi.
Tridiagonal matrix solver
Linear algebra. CMNA functions: tridiagmatrix.
Linear interpolation
Interpolation and extrapolation. CMNA functions: linterp.
Polynomial interpolation
Interpolation and extrapolation. CMNA functions: polyinterp.
Piecewise linear interpolation
Interpolation and extrapolation. CMNA functions: pwiselinterp.
Cubic spline
Interpolation and extrapolation. CMNA functions: cubicspline.
Quadratic Bézier curve
Interpolation and extrapolation. CMNA functions: qbezier.
Cubic Bézier curve
Interpolation and extrapolation. CMNA functions: cbezier.
Bilinear interpolation
Interpolation and extrapolation. CMNA functions: bilinear.
Nearest neighbor
Interpolation and extrapolation. CMNA functions: nn.
Nearest-neighbor image resizing
Interpolation and extrapolation. CMNA functions: resizeImageNN.
Bilinear image resizing
Interpolation and extrapolation. CMNA functions: resizeImageBL.
Finite difference
Differentiation. CMNA functions: findiff.
Symmetric difference
Differentiation. CMNA functions: symdiff.
Right difference
Differentiation. CMNA functions: rdiff.
Second derivative
Differentiation. CMNA functions: findiff2.
Midpoint rule
Numerical integration. CMNA functions: midpt.
Trapezoid rule
Numerical integration. CMNA functions: trap.
Simpson's rule
Numerical integration. CMNA functions: simp.
Simpson's 3/8 rule
Numerical integration. CMNA functions: simp38.
Gaussian integration driver
Numerical integration. CMNA functions: gaussint.
Gauss-Hermite quadrature
Numerical integration. CMNA functions: gauss.hermite.
Gauss-Laguerre quadrature
Numerical integration. CMNA functions: gauss.laguerre.
Gauss-Legendre quadrature
Numerical integration. CMNA functions: gauss.legendre.
Recursive adaptive integration
Numerical integration. CMNA functions: adaptint.
Romberg integration
Numerical integration. CMNA functions: romberg.
Monte Carlo integration, 1D
Numerical integration. CMNA functions: mcint.
Monte Carlo integration, 2D
Numerical integration. CMNA functions: mcint2.
Shell method for volume
Numerical integration. CMNA functions: shellmethod.
Disc method for volume
Numerical integration. CMNA functions: discmethod.
Gini coefficient
Numerical integration. CMNA functions: giniquintile.
Bisection method
Root finding. CMNA functions: bisection.
Newton's method
Root finding. CMNA functions: newton.
Secant method
Root finding. CMNA functions: secant.
Golden-section maximum
Optimization. CMNA functions: goldsectmax.
Golden-section minimum
Optimization. CMNA functions: goldsectmin.
Gradient descent
Optimization. CMNA functions: gd, gdls, graddsc.
Gradient ascent
Optimization. CMNA functions: gradasc.
Hill climbing
Optimization. CMNA functions: hillclimbing.
Simulated annealing
Optimization. CMNA functions: sa.
Traveling salesperson by simulated annealing
Optimization. CMNA functions: tspsa.
Euler method
Differential equations. CMNA functions: euler.
Midpoint method for IVPs
Differential equations. CMNA functions: midptivp.
Fourth-order Runge-Kutta
Differential equations. CMNA functions: rungekutta4.
Adams-Bashforth
Differential equations. CMNA functions: adamsbashforth.
Euler method for systems
Differential equations. CMNA functions: eulersys.
Heat equation, 1D
Differential equations. CMNA functions: heat.
Wave equation, 1D
Differential equations. CMNA functions: wave.
Boundary-value examples
Differential equations. CMNA functions: bvpexample, bvpexample10.
Wilkinson's polynomial
Twenty perfectly ordinary integer roots and a frankly unreasonable sensitivity to small perturbations.
Hilbert matrix
Every entry looks harmless. The linear system does not.
Runge's function
A smooth function that teaches high-degree polynomial interpolation some humility.
The cancellation-prone quadratic
The algebra is correct. One subtraction is still a terrible idea.
Himmelblau's function
Four minima, one landscape, and several ways for a starting point to make the decision for us.
The oscillatory integral
A lot can happen between two perfectly reasonable sample points.
The narrow peak
A smooth integrand can still hide most of its area in a very small neighborhood.
Euler's decay trap
The differential equation decays peacefully. A bad step size does not have to.