An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

Some improvements of invertibility verifications for second-order linear elliptic operators ⋮ Efficient approaches for verifying the existence and bound of inverse of linear operators in Hilbert spaces ⋮ A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator ⋮ Equilibrium validation in models for pattern formation based on Sobolev embeddings

INTLAB

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A priori error estimates for Lagrange interpolation on triangles.
Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse
Non-symmetric low-index solutions for a symmetric boundary value problem
A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration
Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
Computer-assisted methods for the study of stationary solutions in dissipative systems, applied to the Kuramoto-Sivashinski equation
Some remarks on the behaviour of the finite element solution in nonsmooth domains
Numerical verification method for infinite dimensional eigenvalue problems
A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions
On error estimation of finite element approximations to the elliptic equations in nonconvex polygonal domains
Numerical verification of stationary solutions for Navier-Stokes problems
Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications
On very accurate enclosure of the optimal constant in the a priori error estimates for \(H_0^2\)-projection
Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance
On the best constant in the error bound for the \(H_0^1\)-projection into piecewise polynomial spaces
Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains
Numerical verification of solutions for nonlinear elliptic problems using an \(L^\infty\) residual method
Error estimation with guaranteed accuracy of finite element method in nonconvex polygonal domains.
A numerical verification of nontrivial solutions for the heat convection problem
Numerical verification of existence and inclusion of solutions for nonlinear operator equations
Some considerations of the invertibility verifications for linear elliptic operators
Rigorous computation of smooth branches of equilibria for the three dimensional Cahn-Hilliard equation
A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems
Determination of the Babuska-Aziz constant for the linear triangular finite element
Two novel methods and multi-mode periodic solutions for the Fermi-Pasta-Ulam model
Norm bound computation for inverses of linear operators in Hilbert spaces
NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators
Rigorous Numerics in Dynamics
A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations
Verified Eigenvalue Evaluation for the Laplacian over Polygonal Domains of Arbitrary Shape
Efficient Rigorous Numerics for Higher-Dimensional PDEs via One-Dimensional Estimates
Validated Continuation for Equilibria of PDEs
Global smooth solution curves using rigorous branch following
A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow
On theL²a PrioriError Estimates to the Finite Element Solution of Elliptic Problems with Singular Adjoint Operator
A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations
Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces