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COS Method

K_COS_Monograph.tex

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1 \documentclass[11pt,oneside,openany]{book}
2 \usepackage{monograph}
3 \begin{document}
4 \hypersetup{pageanchor=false}
5 \monocover
6 \frontmatter
7 \monotitle
8 \hypersetup{pageanchor=true}
9 \input{frontmatter}
10 \clearpage
11 \tableofcontents
12 \clearpage
13 \mainmatter
14 \monopart{part:gaussian}{Gaussian quadratic forms}{A Gaussian quadratic form has several equivalent representations. We begin with the laws they describe, the hypotheses that make them equivalent, and a small calculation that will accompany the development.}
15 \input{chapters/01_gaussian}
16 \monopart{part:operators}{Structured operators and spectral recovery}{The factor need not fit in memory, and not every part of its action is relevant to a given query. Exact streaming, phase structure, and range compression address these questions separately. Spectral bounds account for what a reduction leaves unresolved.}
17 \input{chapters/02_streaming}
18 \input{chapters/03_phases}
19 \input{chapters/04_range}
20 \input{chapters/05_spectrum}
21 \addtocontents{toc}{\protect\newpage}
22 \monopart{part:kcos}{The K-COS method}{With a spectrum in hand, the problem becomes a tail calculation. Exponential tilting changes its numerical scale. Centered packets simplify the transform on the chosen grid. Separate bounds account for packet approximation, finite support, and omitted modes.}
23 \input{chapters/06_packets}
24 \input{chapters/07_inversion}
25 \input{chapters/08_adaptive}
26 \monopart{part:certified}{Certified numerical computation}{A remainder theorem concerns exact arithmetic. A numerical enclosure must also contain the arithmetic used to evaluate the approximation. This part connects those obligations, states the acceptance rule, and examines the evidence and limits of the implementation.}
27 \input{chapters/09_intervals}
28 \input{chapters/10_accuracy}
29 \input{chapters/11_evidence}
30 \input{chapters/12_synthesis}
31 \appendix
32 \bookmarksetup{startatroot}
33 \input{chapters/A_atlas}
34 \bookmarksetup{startatroot}
35 \input{chapters/B_lean}
36 \bookmarksetup{startatroot}
37 \input{chapters/C_reproduction}
38 \bookmarksetup{startatroot}
39 \input{chapters/D_glossary}
40 \bookmarksetup{startatroot}
41 \input{references}
42 \end{document}

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