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Next, we investigate weighted frames, in particular their relation to controlled frames. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers. Finally, we analyze weighted frames numerically. First, we investigate three possibilities for finding weights in order to tighten a given frame, i.e. decrease the frame bound ratio. Then, we examine Gabor frames and how well the canonical dual of a weighted frame is approximated by the inversely weighted dual frame. <\/jats:p>","DOI":"10.1142\/s0219691310003377","type":"journal-article","created":{"date-parts":[[2010,2,24]],"date-time":"2010-02-24T21:14:11Z","timestamp":1267046051000},"page":"109-132","source":"Crossref","is-referenced-by-count":70,"title":["WEIGHTED AND CONTROLLED FRAMES: MUTUAL RELATIONSHIP AND FIRST NUMERICAL PROPERTIES"],"prefix":"10.1142","volume":"08","author":[{"given":"PETER","family":"BALAZS","sequence":"first","affiliation":[{"name":"Acoustics Research Institute, Austrian Academy of Sciences, Wohllebengasse 12-14, A-1040 Vienna, Austria"}]},{"given":"JEAN-PIERRE","family":"ANTOINE","sequence":"additional","affiliation":[{"name":"Institut de Physique Th\u00e9orique, Universit\u00e9 Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium"}]},{"given":"ANNA","family":"GRYBO\u015a","sequence":"additional","affiliation":[{"name":"NuHAG, Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090, Austria"},{"name":"Faculty of Applied Mathematics, AGH University of Science and Technology, Al. 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