discrete88682

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1、DiscretelinearizedleastsquaresrationalapproximationontheunitcircleMarcVanBarelandAdhemarBultheelDepartmentofComputerScienceK.U.LeuvenFebruary23,1999AbstractWealreadygeneralizedtheRutishauser-Gragg-Harrod-Reichelalgorithmfordiscreteleastsquarespolynomialapproximationonthere

2、alaxistotherationalcase.Inthispaper,anewmethodfordiscreteleastsquareslinearizedrationalapproximationontheunitcircleispresented.ItgeneralizesthealgorithmofReichel-Ammar-Graggfordiscreteleastsquarespolynomialapproximationontheunitcircletotherationalcase.Thealgorithmisfastint

3、hesensethatitrequiresordermcomputationtimewheremisthenumberofdatapointsandisthedegreeoftheapproximant.Wedescribehowthisalgorithmcanbeimplementedinparallel.Examplesillustratethenumericalbehaviorofthealgorithm.Keywords:rationalinterpolation,rationalapproximation,linearizedl

4、eastsquares,(block)unitaryHes-senberg,(block)Schurparameters,(block)orthonormalpolynomials,parallelAMS(MOS)Classication:Primary:41A20,Secondary:65D05,65D15,30E10DiscretelinearizedleastsquaresrationalapproximationontheunitcircleMarcVanBarelandAdhemarBultheelDepartmentofCom

5、puterScienceK.U.LeuvenFebruary23,1999AbstractWealreadygeneralizedtheRutishauser-Gragg-Harrod-Reichelalgorithmfordiscreteleastsquarespolynomialapproximationontherealaxistotherationalcase.Inthispaper,anewmethodfordiscreteleastsquareslinearizedrationalapproximationontheunitci

6、rcleispresented.ItgeneralizesthealgorithmofReichel-Ammar-Graggfordiscreteleastsquarespolynomialapproximationontheunitcircletotherationalcase.Thealgorithmisfastinthesensethatitrequiresordermcomputationtimewheremisthenumberofdatapointsandisthedegreeoftheapproximant.Wedescri

7、behowthisalgorithmcanbeimplementedinparallel.Examplesillustratethenumericalbehaviorofthealgorithm.1IntroductionInourpreviouspublications[14,15],weinvestigatedtherationalinterpolationproblemnotonlyforscalarfunctionvaluesbutalsoforthevectorcase.Thestandpointwetookwasatheoret

8、icalone.Wefoundaparametrizationofallsolutionsoftherationalinterpolationproblemandfastalgo