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updated almost 9 years ago

Quadrature rules for spherical volume integrals by Greg von Winckel

Greg von Winckel

Computes weights and nodes for numerically solving spherical volume integrals. (integration, gauss, quadrature)

[r,t,p,w]=spherequad(nr,nt,np,rad)

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updated 9 years ago

n-dimensional simplex quadrature by Greg von Winckel

Greg von Winckel

% Construct Gauss points and weights for a n-dimensional simplex (integration, guass quadature, simplex)

[X,W]=simplexquad(varargin)

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updated 9 years ago

Gaussian Quadrature for Triangles by Greg von Winckel

Greg von Winckel

Compute Gauss nodes and weights for a triangle (integration, triangle, triangular)

[X,Y,Wx,Wy]=triquad(N,v)

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updated 9 years ago

Gauss Quadrature for Tetrahedra by Greg von Winckel

Greg von Winckel

Compute Gauss weights and nodes for a specied tetrahedron (integration, gauss quadrature, tetrahedron)

[X,Y,Z,W]=tetraquad(N,vert)

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updated 9 years ago

Summed Newton-Cotes Rules by Greg von Winckel

Greg von Winckel

2-11 Point Summed Newton-Cotes Rules (integration, summed newtoncotes, numerical)

Q=cotes(f,a,b,N,nodes)

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updated 9 years ago

Hermite Quadrature by Greg von Winckel

Greg von Winckel

Computes the Hermite weights for user-defined nodes. (integration, hermite, interpolation)

[H0,H1]=hermquad(x)

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updated 9 years ago

Fast Chebyshev Differentiation by Greg von Winckel

Greg von Winckel

Computes the numerical derivative on the Chebyshev grid. (approximation, interpolation, chebyshev)

Dx=fastdiff(x);

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updated 9 years ago

Arbitrary Rank Update to Cholesky Factorization by Greg von Winckel

Greg von Winckel

Solves the Cholesky factored system with arbitrary update. (linear algebra, cholesky, symmetric)

x=cholrankup(R,U,V,b)

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updated 9 years ago

Rank-2 update to LU Factorization by Greg von Winckel

Greg von Winckel

Solve an LU-factorized system with rank-2 update. (linear algebra, rank2, update)

x=lurank2(L,U,u1,v1,u2,v2,b)

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updated 9 years ago

Radial Quadrature and Spectral Methods by Greg von Winckel

Greg von Winckel

Weights, nodes, and spectral methods matices for radial problems (integration, radial, equations)

[r,w,P,Bs,Ds,Dp]=radialquad(N,k,R)

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updated 9 years ago

1-D Unstructured Finite Differences by Greg von Winckel

Greg von Winckel

Computes 3-, 5-, and 7-point FD matrices for unstructured grids (differential equation..., 1d, finite)

[D,D2]=fd3pt(x)

[D,D2]=fd5pt(x)

[D,D2]=fd7pt(x)

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updated almost 10 years ago

Gegenbauer-Gauss-Lobatto Quadrature by Greg von Winckel

Greg von Winckel

Computes weights and nodes for Gegenbauer-Gauss-Lobatto quadrature. (integration, gegenbauer ultraspher..., numerical)

[x,w,C]=gglnodes(N,a)

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updated almost 10 years ago

Fast Chebyshev Transform (1D) by Greg von Winckel

Greg von Winckel

Transfroms between nodal and spectral values. (approximation, interpolation, fast)

B=fcgltran(A,direction)

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updated almost 10 years ago

Conformally Mapped Laplacian by Greg von Winckel

Greg von Winckel

Compute eigenfunctions of the laplacian on a conformally mapped square. (differential equation..., laplacian, eigenfunctions)

sqdirichlet(N,f);

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updated almost 10 years ago

Fast Clenshaw-Curtis Quadrature by Greg von Winckel

Greg von Winckel

Computes Clenshaw Curtis weights and nodes using the FFT. (integration, numerical integration, clenshawcurtis)

[x,w]=fclencurt(N1,a,b)

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updated almost 10 years ago

Numerical Integration on an Arbitrary Grid by Greg von Winckel

Greg von Winckel

Computes weights for numerical integration on arbitrary grid points. (integration, numerical, interation)

A=arbquad(x)

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updated 10 years ago

Bessel Function Zeros by Greg von Winckel

Greg von Winckel

Computes the first k zeros of the Bessel Function of the 1st and 2nd Kinds. (zeros, bessel functions, first)

x=besselzero(n,k,kind)

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updated 10 years ago

Weighted Grid Points by Greg von Winckel

Greg von Winckel

Computes the Lobatto points for an arbitrary weight. (approximation, interpolation, pseudospectral)

[xg,D]=wgrid(w,N)

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updated 10 years ago

2D Wavepacket Time Evolution by Greg von Winckel

Greg von Winckel

Simulates a Gaussian wavepacket in a square domain. (chemistry, physics, quantum wavepacket ti...)

B=fcgltran2d(A,direction)

[p]=barylag2d(f, xn, yn, xf, yf)

wavepacket2d(N,dt)

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updated 10 years ago

Pseudospectral Differentiation on an Arbitrary Grid by Greg von Winckel

Greg von Winckel

Numerically differentiates a function on an arbitrary grid. (differential equation..., pseudospectral, collocation)

D=collocD(x);

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updated 10 years ago

2D Barycentric Lagrange Interpolation by Greg von Winckel

Greg von Winckel

Interpolates a function on a rectangle. (approximation, interpolation, polynomial)

[p]=barylag2d(f, xn, yn, xf, yf)

interptest.m

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updated 10 years ago

Chebyshev Series Product by Greg von Winckel

Greg von Winckel

Computes the product of two Chebyshev expansions. (approximation, interpolation, chebyshev)

c=chebprod(a,b)

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updated 10 years ago

Series Product by Greg von Winckel

Greg von Winckel

Computes the product of two power series. (power series product ...)

c=seriesprod(a,b);

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updated 10 years ago

Generalized Linear Differential Operator Commutator by Greg von Winckel

Greg von Winckel

Computes commuted expansion coefficients for linear operators. (differential equation..., commutation, relations)

B=commute(A)

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updated 10 years ago

Finite Difference Weights by Greg von Winckel

Greg von Winckel

Computes the finite difference for a uniform grid. (differential equation..., finite, difference)

W=ufdwt(h,pts,order)

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updated 10 years ago

Legendre-Pade Approximation by Greg von Winckel

Greg von Winckel

Computes the Legendre Pade approximation to an analytic function. (approximation, interpolation, legendre)

[ahat,bhat]=legendrepade(f,tol)

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updated 10 years ago

Chebyshev-Pade Approximation by Greg von Winckel

Greg von Winckel

Computes the rational Chebyshev approximation of a function. (approximation, interpolation, chebyshev)

[ahat,bhat]=chebyshevpade(f,tol)

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updated 10 years ago

Legendre Collocation Differentiation by Greg von Winckel

Greg von Winckel

Numerically differentiates functions sampled at the LGL nodes. (differential equation..., legendre, polynomials)

[x,D]=legDc(N);

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updated 10 years ago

Chebyshev to Jacobi Conversion by Greg von Winckel

Greg von Winckel

Converts a Chebyshev polynomial expansion to a Jacobi expansion (approximation, interpolation, chebyshev)

jac=cheb2jac(a,b,cheb)

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updated 10 years ago

Jacobi to Chebyshev Conversion by Greg von Winckel

Greg von Winckel

Converts a Jacobi polynomial expansion to a Chebyshev expansion. (approximation, interpolation, jacobi)

cheb=jac2cheb(a,b,jac)

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updated 10 years ago

Chebyshev to Gegenbauer Conversion by Greg von Winckel

Greg von Winckel

Converts Chebyshev polynomials to Gegenbauer polynomials. (approximation, interpolation, gegenbauer ultraspher...)

geg=cheb2geg(a,cheb)

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updated 10 years ago

Gegenbauer to Chebyshev Conversion by Greg von Winckel

Greg von Winckel

Converts Gegenbauer polynomials to Chebyshev polynomials. (approximation, interpolation, gegenbauer ultraspher...)

cheb=geg2cheb(a,geg)

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updated 10 years ago

Legendre to Chebyshev conversion by Greg von Winckel

Greg von Winckel

Converts Legendre polynomials to Chebyshev polynomials. (approximation, interpolation, chebyshev legendre)

cheb=leg2cheb(leg)

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updated 10 years ago

Chebyshev to Legendre conversion by Greg von Winckel

Greg von Winckel

Converts Chebyshev polynomials to Legendre polynomials. (approximation, interpolation, chebyshev legendre)

leg=cheb2leg(cheb)

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updated 10 years ago

Legendre-Gauss Quadrature Weights and Nodes by Greg von Winckel

Greg von Winckel

Computes the Legendre-Gauss weights and nodes for solving definite integrals. (integration, legendre, quadrature)

[x,w]=lgwt(N,a,b)

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updated 10 years ago

Legende-Gauss-Radau Nodes and Weights by Greg von Winckel

Greg von Winckel

Computes the Legendre-Gauss-Radau nodes and weights. (integration, legendre, radau)

[x,w,P]=lglnodes(N)

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updated 10 years ago

2D Chebyshev Transform by Greg von Winckel

Greg von Winckel

Transforms between 2d nodal and spectral data (chebyshev, orthogonal, polynomial)

B=fcgltran2d(A,direction)

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updated almost 11 years ago

Legende-Gauss-Lobatto nodes and weights by Greg von Winckel

Greg von Winckel

Computes the Legendre-Gauss-Lobatto weights, nodes and vandermonde matrix. (integration, legendre, polynomials)

[x,w,P]=lglnodes(N)

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updated almost 11 years ago

Block tridiagonal solver by Greg von Winckel

Greg von Winckel

Solves block tridiagonal systems of equations. (linear algebra, block, tridiagonal)

x=triblocksolve(A,b,N)

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updated almost 11 years ago

Fast Pentadiagonal System Solver by Greg von Winckel

Greg von Winckel

Solves symmetric and asymmetric pentadiagonal systems. (linear algebra, pentadiagonal, 5band)

x=pentsolve(A,b)

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updated almost 11 years ago

Barycentric Lagrange Interpolating Polynomials and Lebesgue Constant by Greg von Winckel

Greg von Winckel

Computes lagrange interpolating polynomials and Lebesgue function/constant. (approximation, interpolation, barycentric lagrange ...)

L=lebesque(x)

[p]=barylag(data,x)

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updated 11 years ago

Pade' Approximant by Greg von Winckel

Greg von Winckel

Computes coefficients of Pade' Approximants to symbolic functions. (approximation, interpolation, rational)

pade(f,N);

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