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A Quadratic to a Quadratic? This Is New!
Mathematics Teacher: Learning and Teaching PK-12, 2021Using technology to explore a rich task, students must reconcile discrepancies between graphical and analytic solutions. Technological reasons for the discrepancies are discussed.
Michael S. Meagher +2 more
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Convex quadratic relaxations of nonconvex quadratically constrained quadratic programs
Optimization Methods and Software, 2013Nonconvex quadratic constraints can be linearized to obtain relaxations in a well-understood manner. We propose to tighten the relaxation by using second-order cone constraints, resulting in a convex quadratic relaxation. Our quadratic approximation to the bilinear term is compared to the linear McCormick bounds.
John E. Mitchell 0001 +2 more
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On the quadraticity of linear combinations of quadratic matrices
Linear and Multilinear Algebra, 2014Let and be nonzero quadratic matrices and let and be nonzero complex numbers. Necessary and sufficient conditions for the quadraticity of the linear combinations of the form are obtained. Our main results contain many of the results in the literature related to idempotency or involutivity of the linear combinations of idempotent and/or involutive ...
Sakarya Uygulamalı Bilimler Üniversitesi/Kaynarca Seyfettin Selim Meslek Yüksekokulu +4 more
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On the quadratic controllability and quadratic feedback minimality
IEEE Transactions on Automatic Control, 2002In Swei et al. (2000) the quadratic controllability and quadratic feedback minimality of unstructured norm bounded uncertain linear systems have been studied with explicitly verifiable necessary and sufficient solvability conditions in terms of the so-called "essential subsystem." In this note, we give the geometric interpretation of the main results ...
Chu, D., Malabre, M.
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Mathematics of Computation, 2015
We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we computed the class groups of imaginary quadratic fields with 100-, 110-, 120-, and 130-digit ...
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We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we computed the class groups of imaginary quadratic fields with 100-, 110-, 120-, and 130-digit ...
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Bilevel Quadratic Fractional/Quadratic Problem
2015The bilevel programming problems are useful tools for solving the hierarchy decision problems. The purpose of this paper is to find the optimality conditions and a solution procedure to solve a bilevel quadratic fractional-quadratic programming problem in which the leader’s objective is quadratic fractional and the follower’s objective is quadratic ...
Nacéra Maachou, Mustapha Moulaï
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THE QUADRATIC AND DOUBLE QUADRATIC RESIDUE CIPHERS
Cryptologia, 1995In a recent article in this journal Shepherd, Sanders and Stockel compare the quadratic residue cipher (QRC) to the Rivest-Shamir-Adleman (RSA) public key cipher. They discuss a number of advantages of the QRC over the RSA, but also indicate a number of shortcomings. In this paper I attempt to redress some of those supposed shortfalls.
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