title: A multiresolution approach for the convergence acceleration of multivariate curve resolution methods.
abstract: Modern computerized spectroscopic instrumentation can result in high volumes of spectroscopic data. Such accurate measurements rise special computational challenges for multivariate curve resolution techniques since pure component factorizations are often solved via constrained minimization problems. The computational costs for these calculations rapidly grow with an increased time or frequency resolution of the spectral measurements. The key idea of this paper is to define for the given high-dimensional spectroscopic data a sequence of coarsened subproblems with reduced resolutions. The multiresolution algorithm first computes a pure component factorization for the coarsest problem with the lowest resolution. Then the factorization results are used as initial values for the next problem with a higher resolution. Good initial values result in a fast solution on the next refined level. This procedure is repeated and finally a factorization is determined for the highest level of resolution. The described multiresolution approach allows a considerable convergence acceleration. The computational procedure is analyzed and is tested for experimental spectroscopic data from the rhodium-catalyzed hydroformylation together with various soft and hard models.
authors.affiliation: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany.
authors.forename: Mathias
authors.initials: M
authors.lastname: Sawall
authors.affiliation: Leibniz-Institut für Katalyse e.V. an der Universität Rostock, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany.
authors.forename: Christoph
authors.initials: C
authors.lastname: Kubis
authors.affiliation: Leibniz-Institut für Katalyse e.V. an der Universität Rostock, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany.
authors.forename: Armin
authors.initials: A
authors.lastname: Börner
authors.affiliation: Leibniz-Institut für Katalyse e.V. an der Universität Rostock, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany.
authors.forename: Detlef
authors.initials: D
authors.lastname: Selent
authors.affiliation: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany; Leibniz-Institut für Katalyse e.V. an der Universität Rostock, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany. Electronic address: klaus.neymeyr@uni-rostock.de.
authors.forename: Klaus
authors.initials: K
authors.lastname: Neymeyr
keywords: Chemometrics; Factor analysis; Multiresolution methods; Non-negative matrix factorization; Pure component decomposition