Estimating the Quadratic Form x T A ?m x for Symmetric Matrices: Further Progress and Numerical Computations

Marilena Mitrouli, Athanasios Polychronou, Paraskevi Roupa and Ondřej Turek
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Marilena Mitrouli: Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, 15784 Athens, Greece
Athanasios Polychronou: Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, 15784 Athens, Greece
Paraskevi Roupa: Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, 15784 Athens, Greece
Ondřej Turek: Department of Mathematics, University of Ostrava, 701 03 Ostrava, Czech Republic

Mathematics, 2021, vol. 9, issue 12, 1-13

Abstract: In this paper, we study estimates for quadratic forms of the type x T A ? m x , m ? N , for symmetric matrices. We derive a general approach for estimating this type of quadratic form and we present some upper bounds for the corresponding absolute error. Specifically, we consider three different approaches for estimating the quadratic form x T A ? m x . The first approach is based on a projection method, the second is a minimization procedure, and the last approach is heuristic. Numerical examples showing the effectiveness of the estimates are presented. Furthermore, we compare the behavior of the proposed estimates with other methods that are derived in the literature.

Keywords: quadratic form; estimates; upper bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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