Fast heuristic methods for function reconstruction using derivative information

Borwein, Jonathan M.; Limber, Martha N.; Noll, Dominikus

doi:10.1080/00036819508840375

Cited by 8 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the centre is the log barrier of interior point fame! The Fisher case is also explicit -via an integro-differential equation of Ricatti type [17,19]. Figure 6.…”

Section: Convex Analysis: An Advertmentioning

confidence: 99%

See 1 more Smart Citation

Maximum entropy and feasibility methods for convex and nonconvex inverse problems

Borwein

2012

Optimization

View full text Add to dashboard Cite

4 A 'spike' proving the nonnegative cone in L p with 1 ≤ p < ∞ has empty interior. 5 Werner Fenchel (1905-1988). 6 The three entropies and their conjugates. 7 The MRI entropy and its conjugate. 8 f (x) := 1 + x 2 2 and g(x) := − 1 2 − (1−x) 2 2. The least gap is at 1/2 with value 7/4. 9 Fenchel describing φ = f * in 1949. 10 Contents of issue 1 of the first volume of Can. J. Math. in 1949. 11 Comparison of three core entropies. 12 Compressed sensing reconstruction [21]. 13 NASA's Hubble telescope. 14 Reconstruction (via I). Top row: the data. Middle: reconstruction. Bottom: truth and error. 15 (AP) 'zig-zagging' to a point on the intersection of a sphere and line segment. 16 Projection method for circle B and segment A fails inside smaller circle. 17 Projector P A (x) and reflector R A (x) for point x. 18 Veit Elser and Sudoku. 19 Bauschke and Schaad's work. 20 Douglas-Rachford cases. 21 A dynamic Cinderella applet studying trajectories of DR and variants. 22 Applet studying thousands of trajectories simultaneously. Starting points are coloured by distance from the y-axis.

show abstract

“…In the centre is the log barrier of interior point fame! The Fisher case is also explicit -via an integro-differential equation of Ricatti type [17,19]. Figure 6.…”

Section: Convex Analysis: An Advertmentioning

confidence: 99%

“…By waiting to see the form of dual, one can customize ones integration scheme to the problem at hand. Even when this is not the case, one can often use the shape of the dual solution to fashion very efficient heuristic reconstructions that avoid any iterative steps (see [19] and Wendy Huang's 1993 thesis or [11]).…”

mentioning

confidence: 99%

Maximum entropy and feasibility methods for convex and nonconvex inverse problems

Borwein

2012

Optimization

View full text Add to dashboard Cite

show abstract

Minimum Fisher information of moment-constrained distributions with application to robust blind identification

Zivojnovic

1998

Signal Processing

View full text Add to dashboard Cite

The Hausdorff entropic moment problem

Romera

Angulo

Dehesa

2001

Journal of Mathematical Physics

View full text Add to dashboard Cite

Our aim in this paper is twofold. First, to find the necessary and sufficient conditions to be satisfied by a given sequence of real numbers {ωn}n=0∞ to represent the “entropic moments” ∫[0,a][ρ(x)]ndx of an unknown non-negative, decreasing and differentiable (a.e.) density function ρ(x) with a finite interval support. These moments are called entropic moments because they are closely connected with various information entropies (Renyi, Tsallis, …). Second, we outline an efficient method for the reconstruction of the density function from the knowledge of its first N entropic moments.

show abstract

Fast heuristic methods for function reconstruction using derivative information

Cited by 8 publications

References 13 publications

Maximum entropy and feasibility methods for convex and nonconvex inverse problems

Maximum entropy and feasibility methods for convex and nonconvex inverse problems

Minimum Fisher information of moment-constrained distributions with application to robust blind identification

The Hausdorff entropic moment problem

Contact Info

Product

Resources

About