A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Filters
Feasible Interpolation for Polynomial Calculus and Sums-Of-Squares
2020
International Colloquium on Automata, Languages and Programming
Preserved Fulltext
We prove that both Polynomial Calculus and Sums-of-Squares proof systems admit a strong form of feasible interpolation property for sets of polynomial equality constraints. ...
For Sums-of-Squares we rely on the use of Boolean axioms, but for Polynomial Calculus we do not assume their presence. ...
A L P 2 0 2 0 63:4
Feasible Interpolation for Polynomial Calculus and Sums-Of-Squares where r i , t q , u i and v i are arbitrary real polynomials. ...
doi:10.4230/lipics.icalp.2020.63
dblp:conf/icalp/Hakoniemi20
fatcat:uyt7va4gwbdhxfk2krivqpnddy
subject index volumes 141-150
2003
Journal of Computational and Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
scheme
145
459
Differentiability
146
343
Differential approximants
149
457
Differential calculus for p-norms
145
425
Differential calculus for vector norms
145
425
Differential equation ...
large numbers
142
27
Least squares
146
179
Least squares
147
53
Left-definite self-adjoint operator
148
213
Left-definite Sobolev space
148
213
Legendre polynomials
148
213
Legendre ...
147 349 Toeplitz operators 142 441 Total ranking method 146 155 Transformation 143 81 Traveling wave fronts 146 309 Tree 142 61 Triangulation 145 505 Trie 142 27 Trigonometric interpolation ...
doi:10.1016/s0377-0427(02)00844-0
fatcat:tsx7p6iw3jbxda3sdee3cdvooq
Sum-of-squares optimization without semidefinite programming
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We propose a homogeneous primal-dual interior-point method to solve sum-of-squares optimization problems by combining non-symmetric conic optimization techniques and polynomial interpolation. ...
The approach optimizes directly over the sum-of-squares cone and its dual, circumventing the semidefinite programming (SDP) reformulation which requires a large number of auxiliary variables. ...
The authors would like to thank the Associate Editor and the Referees for their constructive feedback. ...
arXiv:1712.01792v3
fatcat:f2rnseczuvci7cc7abjgtct5ba
On the Automatizability of Resolution and Related Propositional Proof Systems
[chapter]
2002
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
This gives a better lower bound for the monotone interpolation of Res(2) and a separation from Resolution as a byproduct. ...
After studying the robustness of the definition, we prove the equivalence between: (i) Resolution is weakly automatizable, (ii) Res(¤ ) is weakly automatizable and (iii) Res(¤ ) has feasible interpolation ...
We are grateful to Pavel Pudlák for stimulating discussions on the idea of Theorem 11. ...
doi:10.1007/3-540-45793-3_38
fatcat:vxg4gu2sw5aglizzinrjp6mj74
On the automatizability of resolution and related propositional proof systems
2004
Information and Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
This gives a better lower bound for the monotone interpolation of Res(2) and a separation from Resolution as a byproduct. ...
After studying the robustness of the definition, we prove the equivalence between: (i) Resolution is weakly automatizable, (ii) Res(¤ ) is weakly automatizable and (iii) Res(¤ ) has feasible interpolation ...
We are grateful to Pavel Pudlák for stimulating discussions on the idea of Theorem 11. ...
doi:10.1016/j.ic.2003.10.004
fatcat:sbfnlio72zdonmh2leevz7gveu
The Proof-Search Problem between Bounded-Width Resolution and Bounded-Degree Semi-algebraic Proofs
[chapter]
2013
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The inference rules are typically some more or less obvious, non-interesting, and polynomially checkable ways of producing some logical consequence of the hypotheses. ...
disjunctions and conjunctions, general propositional formulas, polynomial equations over some ring, polynomial inequalities over some ordered ring, disjunctions of those, decision trees branching on variables ...
Acknowledgments We thank the comments of Allen Van Gelder and an anonymous referee on the preliminary draft of this paper. ...
doi:10.1007/978-3-642-39071-5_1
fatcat:4vpknc2xqrbe3fu7hw3nzi7t5m
Proof Complexity (Dagstuhl Seminar 18051)
2018
Dagstuhl Reports
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
NP problem, and in the ensuing decades many powerful techniques have been discovered for analyzing different proof systems. ...
While many longstanding open problems from the 1980s and 1990s still remain unsolved, recent progress gives hope that the area may be ripe for decisive breakthroughs. ...
-Proof Complexity Russell Impagliazzo, Pavel Pudlák, and Jiří Sgall. Lower bounds for the polynomial calculus and the Gröbner basis algorithm. Computational Complexity, 8(2):127-144, 1999. ...
doi:10.4230/dagrep.8.1.124
dblp:journals/dagstuhl-reports/AtseriasNPS18
fatcat:5ksfbo2ehfhspcbuw4ppcuyaqu
Sums of Squares, Moment Matrices and Optimization Over Polynomials
[chapter]
2008
IMA Volumes in Mathematics and its Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Hierarchies of semidefinite relaxations have been proposed in the literature, involving positive semidefinite moment matrices and the dual theory of sums of squares of polynomials. ...
We review the mathematical tools underlying these properties, in particular, some sums of squares representation results for positive polynomials, some results about moment matrices (in particular, of ...
I am very grateful to Markus Schweighofer for discussion and his help with some proofs in the survey, and to Hayato Waki for his careful reading and for his useful questions and suggestions. ...
doi:10.1007/978-0-387-09686-5_7
fatcat:buio7ftpcbfdbdobnaqopag5nu
Behavior Formula Extraction for Object Trajectory using Curve Fitting Method
2014
International Journal of Computer Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
Curve fitting, also known as regression analysis, is used to find the "best fit" line or curve for a series of data points. ...
One of the main goals of computer vision is to enable computers to replicate the basic functions of human vision such as motion perception and scene understanding. ...
the minimum sums of squares for the linear equation do not give minimum sums of squares for the un linear, or original form of the equation. ...
doi:10.5120/18177-9068
fatcat:cv723gdqzfcwdgjb73p6ljjqoa
Interpolant Synthesis for Quadratic Polynomial Inequalities and Combination with EUF
[chapter]
2016
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. ...
theory of concave quadratic polynomial inequalities and the equality theory over uninterpreted functions (EUF). ...
Under a technical condition that if no nonpositive constant combination of nonstrict inequalities is a sum of squares polynomials, then such an interpolant can be generated essentially using the linearization ...
doi:10.1007/978-3-319-40229-1_14
fatcat:bf2mwiy5tvdz3o7jjmdxhatwyi
Complexity of Semialgebraic Proofs
2002
Moscow Mathematical Journal
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2015; you can also visit the original URL.
The file type is application/pdf.
calculus proofs), and Tseitin's tautologies (which are hard for many known proof systems). ...
It is a known approach to translate propositional formulas into systems of polynomial inequalities and consider proof systems for the latter. ...
RM1-2409-ST-02 of the U. S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF). ...
doi:10.17323/1609-4514-2002-2-4-647-679
fatcat:yw73z7hxo5gf5b7fmgf4ijoo7u
subject index 10 volumes
2005
Journal of Computational and Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
180 345
Mesh equidistribution 176 131
Method of feasible direction 175 447
Method of lines 176 293
Method of moments 175 77
m-Function 171 93, 411
Mittag-Leffler functions 171 39
Mixed boundary ...
180 461
Indefinite weight 171 93
Indeterminate moment problems 178 91, 235
Index of determinacy 178 169
Inequalities 172 289
Inequalities of Hardy, Sobolev and Laptev/Weidl
171 59
Inequality constrained ...
doi:10.1016/s0377-0427(05)00274-8
fatcat:lnl66qx5lngarjw7i3ducv7qta
Reviews and Descriptions of Tables and Books
1966
Mathematics of Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
the Leverrier-Faddeev method), least squares, difference tables, polynomial interpolation and numerical differentiation, and finally a brief chapter on ordinary differential equations presenting some ...
Walsh on simultaneous approximation and interpolation by polynomials, and the Stone-Weierstrass theorem. ...
This is a self-instructional manual for FORTRAN II as designed for the IBM 700 series of computers. The material is presented at a very elementary level (high- ...
doi:10.1090/s0025-5718-66-99938-8
fatcat:qoyz4x4e2rdndlhtwi3hse4squ
Galerkin Optimal Control
2016
Journal of Optimization Theory and Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington headquarters Services, Directorate for ...
is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the ...
As with the calculus of variations both necessary and sufficient conditions for optimality may be established. ...
doi:10.1007/s10957-016-0918-x
fatcat:ppa5viqtn5gwrkebxh5aseetkm
Least-squares image resizing using finite differences
2001
IEEE Transactions on Image Processing
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2005; you can also visit the original URL.
The file type is application/pdf.
For a given choice of basis functions, the results of our method are consistently better than those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as ...
The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivatives. ...
Thévenaz, of the Swiss Federal Institute of Technology, for his careful proofreading of this paper. The authors thank also the reviewers for their insightful comments. ...
doi:10.1109/83.941860
pmid:18255551
fatcat:gferpkmuobf6zeugnzw7x2g764
« Previous
Showing results 1 — 15 out of 2,107 results