Pseudospectra have been independently invented at least five times,
as summarized in the table below.
For further information, see [Tre99b].
author 
year 
terminology 
motivation

Henry Landau 
1974 

Landau studied the asymptotic spectra of nonHermitian integral operators
(and, implicitly, the associated Toeplitz matrix eigenvalue problem)
[Lan75]. He later applied these ideas to integral
operators that arise in the study of unstable resonators
[Lan76] and lasers
[Lan77].

Jim Varah 
1977 

Varah was interested in the stability of invariant subspaces of matrices
in the context of numerical solution of nonHermitian
eigenvalue problems
[Var79].

Sergei Godunov, Novosibirsk Group 
1980s 

This research was primarily directed towards developing techniques for
guaranteedaccuracy eigenvalue computations
[GKK90],
[KR85].

Nick Trefethen 
1988 

This work had its roots in observations concerning unstable
eigenvalues of spectral discretization matrices for differential
equations. The first published work concerned polynomial iterative methods
for solving systems of linear algebraic equations
[Tre90]
and spectral methods
[RT90].

Diederich Hinrichsen, Tony Pritchard 
1990 

Hinrichsen and Pritchard originally studied spectral value sets
in control theory [HP92].
In this context, they have been especially interested
in structured perturbations of a matrix.
In the mid1980s, they began studying "stability radii",
a closely related quantity measuring the distance to instability
under specific perturbations.

Other early uses of pseudospectra include
Wilkinson and
Demmel [Dem87a],
who apparently followed the definitions of
Varah [Var79],
and Chatelin, who apparently followed Godunov.
