Expand description
Auto-generated module
🤖 Generated with SplitRS
Functions§
- _use_
helpers - anti_
commutator - Anti-commutator {A, B} = AB + BA.
- app
- app2
- arrow
- banach_
fixed_ point_ iter - banach_
fixed_ point_ ty - banach_
space_ ty - bounded_
linear_ op_ ty - build_
functional_ analysis_ env - bvar
- chebyshev_
coefficients - Chebyshev interpolation coefficients for f on [a,b] at n nodes.
- chebyshev_
nodes - Chebyshev nodes on [a,b].
- chebyshev_
t - Evaluate the n-th Chebyshev polynomial T_n(x) via recurrence.
- closed_
graph_ ty - commutator
- Commutator [A, B] = AB - BA.
- compact_
operator_ ty - condition_
number - Condition number of a matrix (ratio of largest to smallest singular value).
- conjugate_
gradient - cst
- dual_
space_ ty - eval_
chebyshev - Evaluate Chebyshev series at point x on [a,b].
- eval_
fourier_ cosine - eval_
fourier_ sine - Evaluate Fourier sine series at a point.
- fourier_
cosine_ coefficients - fourier_
sine_ coefficients - Compute Fourier sine coefficients on [0, L].
- fredholm_
alternative_ ty - fredholm_
index_ numerical - Check if operator T = I - K is Fredholm by estimating kernel and cokernel dimensions. Returns (kernel_dim, cokernel_dim, index).
- fredholm_
index_ ty - fredholm_
operator_ ty - gauss_
legendre_ 3 - Gauss-Legendre 3-point quadrature on [a,b].
- gauss_
legendre_ composite - Composite Gauss-Legendre 3-point quadrature.
- gauss_
seidel_ iteration - Gauss-Seidel iterative method for solving Ax = b.
- gram_
schmidt - h1_
norm_ approx - Approximate the H^1 Sobolev norm of f on [a,b]: ||f||{H^1}^2 = ||f||{L^2}^2 + ||f’||_{L^2}^2
- h2_
norm_ approx - Approximate the H^2 Sobolev norm (includes second derivative).
- hahn_
banach_ ty - hilbert_
space_ ty - impl_pi
- is_
orthonormal - jacobi_
iteration - Jacobi iterative method for solving Ax = b.
- l2_
inner_ approx - l2_
norm_ approx - lu_
decomposition - Compute LU decomposition with partial pivoting.
- lu_
solve - Solve Ax = b using LU decomposition.
- matrix_
exponential - Matrix exponential via scaling and squaring with Pade approximation.
- nat_ty
- normed_
space_ ty - open_
mapping_ ty - pi
- prop
- qr_
decomposition - Compute QR decomposition of matrix A using modified Gram-Schmidt.
- real_ty
- riesz_
representation_ ty - simpson_
integrate - Simpson’s rule for numerical integration.
- singular_
values - Compute singular values of matrix A (sorted descending).
- spans_
full_ space - spectral_
radius - Approximate spectral radius using power iteration.
- spectral_
theorem_ ty - spectrum_
ty - sup_
norm_ approx - type0
- uniform_
boundedness_ ty