Polynomial Toolbox: polyBox Version 2.0 by Matthew Harker, Paul O'Leary,

Polanomial approximation, polynomials as admissible functions, a comprehensive tutorial. (polynomials, covariance, convolution)

Demonstrate 2: Constrained Polynomials and Beam Measurements

Demonstrate the Constrained Polynomial Approximation

Example of Constrained Polynomials

Vectorized Bisection Search by Sky Sartorius

Find x such that f(x) = target. Vectorization allows for some key advantages over FZERO. (bisection, search, root)

bisection(f,lb,ub,target,options)

N Dimensional Cardinal Spline (Catmull-Rom) Spline Interpolation by Dr. Murtaza Khan

N -Dimensional cubic Cardinal spline (Catmull-Rom) Interpolation (3d, interpolation, cardinal spline)

[MatNbyNPlusOne]=crdatnplusoneval(P0,P1,P2,P3,T,n)

[Pu] =evalcrdnd(P0,P1,P2,P3,T,u)

main.m

Unbounded Resolution for Function Approximation by Alan Jennings

A continuous function is optimized for varying outputs and increasing parameterization dimension (functional, optimization, interpolation)

[Cost_out,CostGrad]=CostFunc_lwr_8(Pnt,Opt)

[Out_out,OutGrad]=OutputFunc_lwr_8(Pnt,Opt)

[PointsOut]=Fmin_ConditionNum(CovIn,N,Opt)

EzyFit 2.41 by Frederic Moisy

A free curve fitting toolbox for Matlab (curve, nonlinear, approximation)

Discover Ezyfit: A free curve fitting toolbox for Matlab

about_ef (Ezyfit Toolbox)

axis0 (Ezyfit Toolbox)

Chebfun by Chebfun Team

Numerical computation with functions instead of numbers. (chebfun, approximation, interpolation)

A greedy algorithm for choosing interpolation points

A keyhole contour integral

A parameter dependent ODE with breakpoints

Simpson's 1/3 and 3/8 rules by Jered Wells

SIMPSON: Simpson's rule for quadratic and cubic numerical integration (numerical, integration, simpsons rule)

simpson(x,y,dim,rule)

SLM - Shape Language Modeling by John D'Errico

Least squares spline modeling using shape primitives (hermite, slm, cubic)

slm_tutorial

hermite2slm(harray)

plotslm(slm)

polyfitn by John D'Errico

Polynomial modeling in 1 or n dimensions (polynomial, curve, regression)

polyfitn_demo

polydern(p,diffvar)

polyfitn(indepvar,depvar,modelterms)

SPLINEFIT by Jonas Lundgren

Fit a spline to noisy data. (approximation, splinefit, cubic spline)

SPLINEFIT EXAMPLES

ppdiff(pp,j)

ppint(pp,a,b)

QUADGR by Jonas Lundgren

Gauss-Legendre quadrature with Richardson extrapolation. (integration, legendre, approximation)

quadgr(fun,a,b,tol,trace,varargin)

ALTSUM by Jonas Lundgren

Convergence acceleration of alternating series. (sum, approximation, mathematics)

altsum(a,method)

Best polynomial approximation in uniform norm by Andrew Knyazev

For a given function on an interval, the code calculates the min-max approximation by a polynomial. (mathematics, statistics, optimization)

polyfitinf(M,N,K,X,Y,EPSH,MAXIT,REF0)

Newton - Raphson method by Andrea Cirillo

Find the zero of a regular function with Newton - Raphsons' method. (newton raphson, zero, newton)

zero=newton_raphson(funzione,tolleranza)

Check Whether a Point Lies Inside,Outside or On a Circle by Divakar Roy

Checks whether a point lies inside,outside or on a circle defined by 3 other points. (circle, inside, approximation)

result=iscircle(X,Y,x,y)

B-spline tools by Jan Tore Korneliussen

Basic toolbox for polynomial B-splines on a uniform grid. OO overloading of common operators. (splines, approximation, interpolation)

B-spline toolbox

bspline0( x )

bspline1( x )

Simpson's Rule Integration by Juan Camilo Medina

Computes an integral "I" via Simpson's rule in the interval [a,b] with n+1 equally spaced points (approximation, integration, simpsons rule)

simpsons(f,a,b,n)

Leibniz Approximation of pi by Ben Nuttall

This program computes the decimal places of pi using Leibniz's formula. Watch them converge! (pi, leibniz, leibniz formula for p...)

pi1.m

pi2.m

pi3.m

Piecewise Hermite Cubic Interpolation by Juan Camilo Medina

Interpolates with a Hermite cubic polynomial using the function values and corresponding derivatives (interpolation, hermite, mathematics)

y=p3hermite(x,pointx,pointy,yprime,plt)

Newton's Method by Harmon Amakobe

Finds better successive approximations for the root of a function using Newton's Method. (newtons method, newton, method)

newt(func,gss,ite,tol)

Bisection's method by Andrea Cirillo

It's a matlab function that finds a regular real function's zero with the bisection's method. (bisection, approximation, optimization)

p_min=bisection(func,int,iter,tol_x,tol_f)

Image and Terrain Modeling using Incremental Delaunay Triangulation by Omid Sakhi

This program model image/digital elevation data using incremental Delaunay triangulations. (image, terrain, modeling)

aIDT(input_im,max_allowed_error,max_number_of_iterations)

aRDT(input_im,number_of_vertex)

aReCon(dt,z)

polyfit3 by Antoni J. Canós

Fit polynomial to data, with new features as forced to zero coefficients and data weighting. (fitting, polynomial fitting, approximation)

polyfit3(x,y,n,nul,w)

Bisection by Wolfgang Putschögl

Computes the root of a function f by bisectioning. (approximation, solve, mathematics)

bisection(f,a,b,delta)

Gradient from Neural Network by Alan Jennings

Function that takes a NN and creates a new NN that gives the gradient. (neural networks, function, gradient)

NN_DerivativeValidate

NN_GradientFunction(net)

Surface Fitting using gridfit by John D'Errico

Model 2-d surfaces from scattered data (interpolation, surface, modeling)

gridfit_demo

gridfit(x,y,z,xnodes,ynodes,varargin)

test_main.m

Line Simplification by Wolfgang Schwanghart

Recursive Douglas-Peucker Polyline Simplification (Iterative Endpoint Fit) (approximations, interpolation, polyline)

dpsimplify(p,tol)

dpsimplify(p,tol)

Cardinal Spline (Catmull-Rom) Spline by Dr. Murtaza Khan

Evaluates and plot 2D Cardinal Spline (Catmull-Rom) Spline. (cardinal spline, catmull, approximation)

[xt,yt] =EvaluateCardinal2D(P0,P1,P2,P3,T,u)

[xvec,yvec]=EvaluateCardinal2DAtNplusOneValues(P0,P1,P2,P3,...

TestEvaluateCardinal2D.m

Spline based function approximation for HDL synthesis by Sean Little

This is a suite of simple utilities that allow for efficient approximation of complex functions in a (hdl, hdl coder, spline)

[x,pp]=create_lut3(fcn, rng, tol)

example

nearestpoint(x,y,m) ;

Matrix Analysis of Three Dimensional Bar Structures MABS3D by Marcos Cesar Ruggeri

This program is an extension of MABS2D to three-dimensional space (3D). (approximation, fea, fem)

mabs3d.m

Triangular Mesh Refinement by Dirk-Jan Kroon

This function will refine a triangular mesh with 4-split spline interpolation (refinement, triangular, interpolation)

Fnew=makenewfacelist(F,HT_index, HT_values)

Ne=vertex_neighbours(FV)

Ne=vertex_neighbours_double(Fa,Fb,Fc,Vx,Vy,Vz)

Sub-Sample Peak Fitting 2D by Eric

Find sub-sample location of global maximum in a 2-dimensional numerical matrix. (approximation, fit, peak)

peakfit2d(Z)

Fast and Robust Curve Intersections by Douglas Schwarz

Computes intersection points of two curves. (approximation, interpolation, intersect intersectio...)

intersections(x1,y1,x2,y2,robust)

NURBS Toolbox by D.M. Spink by Paul Zhang

NURBS Toolbox by D.M. Spink re-uploaded. The previous link has broken. (approximation, bspline, interpolation)

basisfun(i,u,p,U)

bspdegelev(d,c,k,t)

bspderiv(d,c,k)

Matrix Analysis of Two Dimensional Bar Structures MABS2D by Marcos Cesar Ruggeri

This program solves bar structures of constant area through matrix analysis of structures. (matrix analysis, structures, aerodef)

nanderivative.m v2.1 (Jul 2009) by Carlos Adrian Vargas Aguilera

N-order derivative of vector data by interpolating nearby points, ignoring NaNs. (derivative, nan, diff)

nanderivative(Y,X,N,K,MET)

A Numerical Tour of Signal Processing by Gabriel Peyre

A set of Matlab experiments that illustrates advanced computational signal and image processing. (approximation, wavelets, denoising)

[p,ellipse]=phantom(varargin)

b=dct(a,n)

b=dct2(arg1,mrows,ncols)

Thin Plate Spline Network with Radiohead Example by Travis Wiens

Thin plate splines can be used to interpolate nonuniform data, such as the Radiohead dataset, which (thin plate spline, rbf, approximation)

[a, xc]=train_thin_plate_spline(x,y)

y_hat=sim_thin_plate_spline(x,x_c,a);

tps_radiohead_example.m

2D Cubic Beizer Curve by Dr. Murtaza Khan

Evaluate and plot 2D cubic bezier curve for given four control points. (bezier, approximation, cubic)

Funct_Bezier(Px,Py,n)

TestCubicBezier.m

Approximation of Circle Using Cubic Bezier Curve by Dr. Murtaza Khan

Approximation of unit radius circle with four parametrix bezier curves (points, interpolation, bezier)

PlotBezier1(Px,Py,n)

[Qx,Qy]=CubicBezier1(Px,Py,n)

TestCircleApproxByCubicBezier.m

Approximation of 2-D Data by Natural Cubic Spline by Dr. Murtaza Khan

Approximation (Data Fitting) by Natural Cubic Spline. (approximation, interpolation, natural cubic spline)

SquareDistance=TwoNormSqDist(p1,p2)

[bx,by,finalbreaks,MaxSqDist]=ncs2dapprox(x,y,varargin)

[fx,fy,index]=MergeSortRemoveDuplicates(fxSet1,fySet1,Set1i...

Bezier Interpolation in N-Dimension Space by Dr. Murtaza Khan

Bezier interpolation for given four control points. Each control point can be in N-Dimensional. (3d, n dimension, bezier)

[Q]=bezierInterp(P0,P1,P2,P3,varargin)

bezierInterpTest.m

cubic Bezier least square fitting by Dr. Murtaza Khan

Approximation of data using cubic Bezier curve least square fitting (approximation, interpolation, cubic)

FindBezierControlPointsND(p,varargin)

Q=bezierInterp(P0,P1,P2,P3,varargin)

[MatGlobalInterp]=BezierInterpCPMatSegVec(p0mat,p1mat,p2mat...

ODE Solver through Galerkin Method by Marcos Cesar Ruggeri

This program solves Ordinary Differential Equations by using the Galerkin method. (galerkin, approximation, differential equation...)

[approx,exac,err]=odegalerkin(poly,cc,n)

Richardson Extrapolation by Rhys

A generalized Richardson extrapolation routine with many bells and whistles. (extrapolation, approximation, taylor)

richardson( A1s, kis, t, exact )

Calculate roots of Chebyshev polynomials. by Russell Francis

Calculate the roots of a Chebyshev polynomial of arbitrary degree. (chebyshev, root, approximation)

ChebyshevRoots( n, type, range )

interpsinc.m by Michael Minardi

This M-File interpolates a sampled function using sin(x)/x (approximation, interpolation, interpolate)

interpsinc(xi,f,varargin)

vebyk by Rolf Sidler

vebyk performs ordinary kriging and can be easily adapted to other kriging methods. (kriging, 2d, approximation)

buildbigc3(position,anisotropy,nu,range)

buildsmallc3(position,anisotropy,nu,range)

covcalc(lag,nu,a)

Single-variable linear level finding ("inverse" INTERP1): findX by Antoni J. Canós

Estimates the XI values at which the dependent variables Y reach a specified level YI. (interpolation, data exploration, mathematics)

findX(X,Y,YI)

smooth2a by Greg Reeves

Smooths a 2D matrix using a mean filter over a user-defined rectangle. Ignores and preserves NaNs. (2d, approximation, interpolation)

smooth2a(matrixIn,Nr,Nc)