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20 Sep 2023: computational analysis Compute spectral properties rigorously, practically! • Continuous linear algebra Avoid the woes of discretization. • ... 16] Colbrook, Matthew J. "On the computation of geometric features of spectra of linear operators on

19 Sep 2023: computational analysis Compute spectral properties rigorously, practically! • Continuous linear algebra Avoid the woes of discretization. • ... 16] Colbrook, Matthew J. "On the computation of geometric features of spectra of linear operators on

9 Feb 2023: 2021). 12/38. Echoes of an old story. Hilbert’s vision (start of 20th century): secure foundations for all mathematics. ... I True statements in mathematics that cannot be proven! I Computational problems that cannot be computed by an algorithm!

28 Nov 2023: 1. INTRODUCTION. Finite dimensional inverse problems are ubiquitous in the computational sciences as they naturally appearin a plethora of applications. ... 5. RELATION TO PREVIOUS WORK. As an ongoing topic of research in many areas of mathematics,

20 Nov 2023: This is a classification hierarchy for all types of prob-lems in computational mathematics that allows for classifications determining the boundaries of what algorithmscan achieve. ... The SCI hierarchy captures many key computational issues in the

18 Dec 2023: Remark 1.3 (Trustworthiness of algorithms). By ’trustworthy algorithm’ for a computational problem, we meanthe following. ... Condition in optimisation: Condition numbers in computational mathematics and numerical analysis have beena mainstay [27, 39]

19 Nov 2023: e. the number of computational steps, and ‘space’i.e. the amount of computer memory workspace needed. ... Our discussion of computational complexity above shows that thelatter is surely the way to go!

18 Dec 2023: Hence, we assume that algorithms accessthe input to whatever finite precision desired and that all computational operations are done exactly. ... It is also a part of broader efforts to establishthe mathematics behindthe Solvability Complexity Index (SCI)

11 Jan 2023: Mathematics Subject Classification: 65K0, 65B99, 68Q25, 90C25, 90C60. 1 Introduction. First-order methods are the workhorse of much of modern continuous optimization [6, 10, 24, 59].They are widely used to ... The main difference is theinclusion of the

7 Mar 2023: Forour computational problems, this allows:. 5. (P1) Computation of spectra and approximate eigenstates with guaranteed error control. ... There is an increased computational cost for smaller , which typically requireslarger truncation parameters.