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## SUMMARY OF PARAMETRIC IMAGE REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0007
- Subject:
- Mathematics, Applied Mathematics

This chapter summarizes the techniques discussed so far in this book. The techniques are all based on the minimization of a certain distance measure, and the distance measure is based on image ... More

## SPECTRALLY CONSTRAINED APPROXIMATION

*Moody T. Chu and Gene H. Golub*

### in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566649
- eISBN:
- 9780191718021
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566649.003.0007
- Subject:
- Mathematics, Applied Mathematics

This chapter shows that the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. A general ... More

## OPTIMAL LINEAR REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0006
- Subject:
- Mathematics, Applied Mathematics

This chapter investigates the question of how to find an optimal linear transformation based on a distance measure. Popular choices for distance measures such as the sum of squared differences, ... More

## Convex Optimization and Numerical Issues

*Pierre-Loïc Garoche*

### in Formal Verification of Control System Software

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691181301
- eISBN:
- 9780691189581
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181301.003.0010
- Subject:
- Mathematics, Applied Mathematics

This chapter aims at providing the intuition behind convex optimization algorithms and addresses their effective use with floating-point implementation. It first briefly presents the algorithms, ... More

## Definitions—Background

*Pierre-Loïc Garoche*

### in Formal Verification of Control System Software

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691181301
- eISBN:
- 9780691189581
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181301.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter presents the formalisms describing discrete dynamical systems and gives an overview on the convex optimization tools and methods used to compute the analyses. A dynamical system is a ... More

## Optimal Control Imaging of Extended Inclusions

*Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab*

### in Mathematical Methods in Elasticity Imaging

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.003.0010
- Subject:
- Mathematics, Applied Mathematics

This chapter describes the use of time-reversal imaging techniques for optimal control of extended inclusions. It first considers the problem of reconstructing shape deformations of an extended ... More

## Parameter Optimization

*John E. Prussing*

### in Optimal Spacecraft Trajectories

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198811084
- eISBN:
- 9780191848360
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198811084.003.0002
- Subject:
- Mathematics, Applied Mathematics

Parameter optimization is treated as an introduction. Unconstrained and constrained cases are analysed. Necessary and sufficient conditions are derived and illustrated. Parameter optimization ... More

## Optimal Control Theory

*John E. Prussing*

### in Optimal Spacecraft Trajectories

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198811084
- eISBN:
- 9780191848360
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198811084.003.0004
- Subject:
- Mathematics, Applied Mathematics

Optimal Control Theory is reviewed in detail. We consider a dynamic system that operates between a specified initial time and a final time which may be specified or unspecified. Necessary conditions ... More

## Invariant Synthesis via Convex Optimization: Postfixpoint Computation as Semialgebraic Constraints

*Pierre-Loïc Garoche*

### in Formal Verification of Control System Software

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691181301
- eISBN:
- 9780691189581
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181301.003.0005
- Subject:
- Mathematics, Applied Mathematics

This chapter focuses on the computation of invariant for a discrete dynamical system collecting semantics. Invariants or collecting semantics properties are properties preserved along all executions ... More

## Template-based Analyses and Min-policy Iteration

*Pierre-Loïc Garoche*

### in Formal Verification of Control System Software

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691181301
- eISBN:
- 9780691189581
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181301.003.0006
- Subject:
- Mathematics, Applied Mathematics

This chapter considers other configurations aside from the direct synthesis of invariants as bound templates. A first case arises when the methods shown in the previous chapter only synthesizes the ... More

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