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Highlights from
regtools

• app_hh(A,beta,v) APP_HH Apply a Householder transformation.
• art(A,b,k) ART Algebraic reconstruction technique (Kaczmarz's method).
• baart(n) BAART Test problem: Fredholm integral equation of the first kind.
• bidiag(A) BIDIAG Bidiagonalization of an m-times-n matrix with m >= n.
• blur(N,band,sigma) BLUR Test problem: digital image deblurring.
• cgls(A,b,k,reorth,s) CGLS Conjugate gradient algorithm applied implicitly to the normal equations.
• cgsvd(A,L) CGSVD Compact generalized SVD of a matrix pair in regularization problems.
• corner(rho,eta,fig) CORNER Find corner of discrete L-curve via adaptive pruning algorithm.
• csvd(A,tst) CSVD Compact singular value decomposition.
• deriv2(n,example) DERIV2 Test problem: computation of the second derivative.
• discrep(U,s,V,b,delta,x_0) DISCREP Discrepancy principle criterion for choosing the reg. parameter.
• dsvd(U,s,V,b,lambda) DSVD Damped SVD and GSVD regularization.
• fil_fac(s,reg_param,method,s1... FIL_FAC Filter factors for some regularization methods.
• foxgood(n) FOXGOOD Test problem: severely ill-posed problem.
• gcv(U,s,b,method) GCV Plot the GCV function and find its minimum.
• gcvfun(lambda,s2,beta,delta0,...
• gen_form(L_p,x_s,A,b,K,M) GEN_FORM Transform a standard-form problem back to the general-form setting.
• gen_hh(x) GEN_HH Generate a Householder transformation.
• get_l(n,d) GET_L Compute discrete derivative operators.
• gravity(n,example,a,b,d) GRAVITY Test problem: 1-D gravity surveying model problem
• heat(n,kappa) HEAT Test problem: inverse heat equation.
• i_laplace(n,example) I_LAPLACE Test problem: inverse Laplace transformation.
• l_corner(rho,eta,reg_param,U,... L_CORNER Locate the "corner" of the L-curve.
• l_curve(U,sm,b,method,L,V) L_CURVE Plot the L-curve and find its "corner".
• lagrange(U,s,b,more) LAGRANGE Plot the Lagrange function for Tikhonov regularization.
• lanc_b(A,p,k,reorth) LANC_B Lanczos bidiagonalization.
• lcfun(lambda,s,beta,xi,fifth) Auxiliary routine for l_corner; computes the NEGATIVE of the curvature.
• lsolve(L,y,W,T) LSOLVE Utility routine for "preconditioned" iterative methods.
• lsqi(U,s,V,b,alpha,x_0) LSQI Least squares minimizaiton with a quadratic inequality constraint.
• lsqr_b(A,b,k,reorth,s) LSQR_B Solution of least squares problems by Lanczos bidiagonalization.
• ltsolve(L,y,W,T) LTSOLVE Utility routine for "preconditioned" iterative methods.
• maxent(A,b,lambda,w,x0) MAXENT Maximum entropy regularization.
• mr2(A,b,k,reorth) MR2 Solution of symmetric indefinite problems by the MR-II algorithm
• mtsvd(U,s,V,b,k,L) MTSVD Modified truncated SVD regularization.
• ncp(U,s,b,method) NCP Plot the NCPs and find the one closest to a straight line.
• ncpfun(lambda,s,beta,U,dsvd)
• nu(A,b,k,nu,s) NU Brakhage's nu-method.
• parallax(n) PARALLAX Stellar parallax problem with 28 fixed, real observations.
• pcgls(A,L,W,b,k,reorth,sm) PCGLS "Precond." conjugate gradients appl. implicitly to normal equations.
• phillips(n) PHILLIPS Test problem: Phillips' "famous" problem.
• picard(U,s,b,d) PICARD Visual inspection of the Picard condition.
• pinit(W,A,b) PINIT Utility init.-procedure for "preconditioned" iterative methods.
• plot_lc(rho,eta,marker,ps,reg... PLOT_LC Plot the L-curve.
• plsqr_b(A,L,W,b,k,reorth,sm) PLSQR_B "Precond." version of the LSQR Lanczos bidiagonalization algorithm.
• pmr2(A,L,N,b,k,reorth) PMR2 Preconditioned MR-II algorithm for symmetric indefinite problems
• pnu(A,L,W,b,k,nu,sm) PNU "Preconditioned" version of Brakhage's nu-method.
• prrgmres(A,L,N,b,k) PRRGMRES Preconditioned RRGMRES algorithm for square inconsistent systems
• quasifun(lambda,s,xi,dsvd)
• quasiopt(U,s,b,method) QUASIOPT Quasi-optimality criterion for choosing the reg. parameter
• regutm(m,n,s) REGUTM Test matrix for regularization methods.
• rrgmres(A,b,k) RRGMRES Range-restricted GMRES algorithm for square inconsistent systems
• shaw(n) SHAW Test problem: one-dimensional image restoration model.
• spikes(n,t_max) SPIKES Test problem with a "spiky" solution.
• spleval(f) SPLEVAL Evaluation of a spline or spline curve.
• splsqr(A,L,b,lambda,Vsp,maxit... SPLSQR Subspace preconditioned LSQR for discrete ill-posed problems.
• splsqr(A,b,lambda,Vsp,maxit,t... SPLSQR Subspace preconditioned LSQR for discrete ill-posed problems.
• std_form(A,L,b,W) STD_FORM Transform a general-form reg. problem into one in standard form.
• tgsvd(U,sm,X,b,k) TGSVD Truncated GSVD regularization.
• tikhonov(U,s,V,b,lambda,x_0) TIKHONOV Tikhonov regularization.
• tomo(N,f) TOMO Create a 2D tomography test problem
• tsvd(U,s,V,b,k) TSVD Truncated SVD regularization.
• ttls(V1,k,s1) TTLS Truncated TLS regularization.
• ursell(n) URSELL Test problem: integral equation wiht no square integrable solution.
• wing(n,t1,t2) WING Test problem with a discontinuous solution.
• Contents.m
• regudemo.m
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