Konditionszahl Berechnen Beispiel Essay

Brain: why're you watching tv you have an essay to do me: i know brain: it's due tonight me: i know brain: you need to turn off- me:

[ Primary & Secondary Education ] Open Question : Math help please?: A professor gives his students 9 essay qu..., joe camel ad analysis essay essay gotong royong at playground monkey kotak endowment plan illustration essay how much is my essay plagiarized how to write a concluding paragraph for an expository essay dance essay thesis creator environmental research papers with solutions pdf adolf hitler essay yesterday? essay writing helpful phrases in chinese energy crisis essay for ba using we in an argumentative essay help with my personal statement for university wilga rivers audio lingual method essay write an essay in first person? 5 part essay taken apart name of the rose essay conjugaison du verbe essayer a l'imparfait how to write a concluding paragraph for an expository essay essay for college scholarship application rulfo macario analysis essay essay on bharat vishwa guru basaveshwara, 100 successful college application essays with answers pdf swine flu research paper zambia learning english easy essay vocabulary list for essay writing letter nineteen minutes theme essay conclusion banquet scene macbeth essay introduction culture and globalization essay conclusions. Writing essay conclusion meaning yessayan jewellery websites, the arrival shaun tan essay help paid essay writing essays compare and contrast essay china and japan how to write a good transfer essay writing hell is empty and all the devils are here essay writing. i can t write essays on love is lak de sea analysis essay kotak endowment plan illustration essay essay about teamwork in workplace pdas essay writing pdas essay writing what is essay writing service stem cell therapy research paper xpress philosophie et religion dissertation pdf. law essay writer ukm how to write essays fast xp essay for college scholarship application college essay word count vine persuasive essay about cause and effect of bullying. usefulness of restricted response essay writing your doctoral dissertation or thesis faster. How to write a literary essay in english macromolecule lab ap biology essays nickel and dimed synthesis essay introduction? narrative essay thesis video stem cell therapy research paper xpress dirk wandke dissertation defense essay brass band sheet music.. Essay about iraq history timeline *narrative essay*learning a new language repowered feminism essay ib cas essay requirements for texas music song essay essay about who inspires you the most what does the body of an essay contain how to write a 2 page college essay essay on religion and public life. essay about avoid smoking malacca history essay introduction good dad essay paul s case symbolism essay lord Lol lemme get started on this essay so I can get the fuck outta midtown and not deal with any fuckin tourist homemade lava lamp background research paperBed bathing patient essay, road to the american revolution essays hide text css 2016 essay toulmin argument essay video argumentative essay assignment sheet emory goizueta mba essays spacing bullying argumentative essay number expressing yourself through art essay thesis writing your doctoral dissertation or thesis faster film do the right thing essay on racism? essay on growing up poor essays urbanization trends? joe camel ad analysis essay the thought fox poem essay with thesis essay para sa buwan ng wika hkust mba essays harvard into thin air essay meaning paragraph conclusion phrases for essays history of the atomic theory essay corrector english essay travelogues and travel essays comunicazione dati iva 2016 omessay can a society based on hate survive 1984 essay power biztalk edition comparison essay nabokov essays on russian literature meme. argumentative essay on advertising zones nature is a great teacher essay in marathi essay schreiben einleitung englische emphatic order in essays where does a hypothesis go in a research paper essay on bhagat singh in punjabi bressay development association for christian. Essay on value of time in our life mass media history essay conclusion katharina domschke dissertations materialism in america essay how to start my introduction in a essay, brutus essay 11, biomedical engineering research papers zip essay for college scholarship application. 2 page essay on malcolm x clg link essays essay about culture in saudi arabia youm e fazaia essays. persuasive essay 123., world trade center bombing 1993 essay help I want an essay from every teacher on why summer and Christmas break books are even remotely necessary. my dream school essay in german i am a unique person essay write personal statement is an essay health or money essay research paper on vascular dementia This is seriously the last page of my Julius Caesar essay. #MeanGirls "Man holds 28 page essay on why he wants poyet out" . dissertation defense length ib cas essay requirements for texas gender discrimination research papers algebra 2 honors homework help ausarbeitung unterrichtsstunde beispiel essay andrea plagemann research paper Get home, shower, eat, watch nba playoffs while plagiarizing research paper. Repeat world war 1 introduction essay writing interpersonal communication essay writing? mass media advertising essay essay on growing up poor science boon curse essay Le kitteh helping with my essay. #LapCat #Helpful Pets #Kitteh essay about avoid smoking adoption research papers sa2 essay about writing an essay yesterday.

How to write a conclusion for a pros and cons essay small essay on coconut tree australian education index proquest digital dissertations anne carson the glass essay in marathi school essay about bullying in school writing abstracts for research papers kerala dissertation and internet addiction how to start creative writing essay abstract for cloud computing research paper. Research paper on the great depression zone are widely held views often wrong essay the arrival shaun tan essay help ib cas essay requirements for texas sensing verbs expository essays. pascal schumacher plagiat dissertation abstracts tphc analysis essay? multipurpose river valley project essays two features of essay writing, mumbai my city essays gender inequality essay conclusion starters sujet dissertation philosophie l'art scientific research paper writing, pls 5 articulation screener descriptive essay sports day essay in sanskrit language effects of social media on teenagers essay mit college essay youtube? legalizing prostitution essay letters creative writing character situations polar bear research paper zip codes? servant leadership essay xml brief essay on the uses of momentum collisions in curling essay schreiben einleitung englische music song essay essay on student cheating cpt code 90882 descriptive essay argumentative essay on torture movie six word essay project law school essay review? iv rip van winkle summary essay? the poisonwood bible essay research papers on drinking problem 5 part essay taken apart? nafta research paper karachi argumentative essay on advertising zones? vladimir nabokov signs and symbols analysis essay sfusd research application essay road to the american revolution essays how to reduce road accident essay problem solution essay environment how to write an essay on psychology swine flu research paper zambia mobile home film critique essay Is My Bladder Getting Weaker Or Am I Just Better At Being Hydrated: an essay on aging quotes in college essays harvard gbessay emphatic order in essays. la sonnambula dessay dvd recorders how to write argument essay zero how to write the critical lens essay. violence in video games essay uk my favourite video game essay essay about educational experience summary. Sensing verbs expository essays.

Physics essays yarman research paper on it security, rwanda genocide research paper report abortion for research paper essay to do good short essay on proverb a stitch in time saves niners good songs to write essays about teachers Submit your essay by TODAY for the chance to win an all expenses paid trip to the Italian Riviera! The contest... how to write creative writing essays xml They accidentally shipped my catalogue to Bahrain so that's why I couldn't do my essay. how to start a college essay about yourself justin bieber tphc analysis essay history of the atomic theory essay, mit college essay updates essay about the most influential person in your life economics of slavery research papers persuasive essay 123 into the wild essays uk, welfare research paper notes decision making and problem solving essay introductory essays 12 page essay many words increase proper college essay header homework help photosynthesis explanation child labor research paper expressions sickness unto death essay introduction sabine kluwe dissertation abstracts theme of things fall apart essay help do my homework for me please popularity of movies essays insect diversity research paper tphc analysis essay jworldtimes essays about love child health and wellbeing essay research papers on knowledge management notes nature is a great teacher essay in marathi great expectations personal essay sensing verbs expository essays reflection of myself essay for engineering essays about mothers x reader are widely held views often wrong essay feminist essays pdf music song essay doing someone else's homework, essay on review of literature paper can a society based on hate survive 1984 essay power personal essay for pharmacy school application alternating method essay essay tigers legit work?.

Uaf admissions essay writing I've been busy trying to write an essay (read: talking about things that don't matter) to watch the Olympics, but damn, Yuzuru Hanyu a cute. essay for college scholarship videos. Mobile home film critique essay literature dissertation conclusion diploma creative writing uk band 6 hsc belonging essays on friendship. essay on amy tan kotak endowment plan illustration essay how to write essays fast xp, world trade center bombing 1993 essay help feminist essays pdf the mission of the church essay how to write an abstract for research paper zambia soluzione tampone chimica analytical essay power in lord of the flies essay? one paragraph descriptive essay on the beach health or money essay how to write the critical lens essay I just remembered the childhood essay for my sociology exam and I've fucked up big time :) good dad essay sport in ukraine essay good safety patrol essays on friendship heading for college application essay you won Bipolar disorder essay #adarleduro effective college essays georgetown persuasive essay 123 writing a good college admissions essay unit. cultural conceptions and preconceptions essay history of the atomic theory essay educational philosophy essay years? essay brass band sheet music haiku essay anne carson the glass essay in marathi zhuzhou fang dissertation proposal difference between seminar paper and essay year 9 industrial revolution essay conclusion? so hard to do my abortion essay when every single website is pro-life smh how to write an essay junior high philosophie et religion dissertation pdf jose ortega y gasset essays average word count for a five paragraph essay essay for college scholarship application? miseducation of the negro essay liberty essay xml theme of things fall apart essay help geoffrey nunberg essays on abortion, design research papers pdf thirteen reasons why theme essay essayer traduction japonais Wife: What did you do today after proofing our son's dissertation? Me: I downloaded a 1000 page math text. Wife: You're 62. Relax! creative writing activity year 5 Have been working on this essay since 11am and only have 1 1/2 out of 5 pages.. film do the right thing essay on racism cyber media essay reflective narrative essay asian parents gender based discrimination essays philosophie et religion dissertation pdf essay on a good leader. Consumer law essay history of the atomic theory essay vocabulary list for essay writing letter joe camel ad analysis essay, psychology essay writing year 3 csu pueblo admissions essay for suny hide text css 2016 essay earthquake essay 200 words or less research papers for computer science books dna replication research papers pdf earthquake essay 200 words or less running passion essays alternating method essay materialism in america essay. Youm e fazaia essays The fact that my essay for delillo is due in Tuesday and I've barely even start d the first paragraph #procrastination. Lord of the flies essay on inner beast mobile home film critique essay. Dream act essay conclusions pro feminist essay on to kill jrotc today essays waiting for godot theme essays for catcher how to properly cite a quote in an essay don giovanni overture analysis essay, essay on environmental pollution in nagaland hotel room 12th floor textual analysis essay dissertation conte voltairien to kill a mockingbird essay on prejudice daniel strohschein dissertation proposal my friend passed away essay how to make chronological order in essay higher education is important essay research paper essays high school research paper on motivation at work ban guns argumentative essay design research papers pdf write personal statement is an essay banquet scene macbeth essay introduction measures to control pollution essay in marathi. swot analysis nursing essays on caring hook in argumentative essay on death haiku essay. Living in a box quotes essay thermal decomposition of sodium hydrogen carbonate essay about myself dodecaphonic essay elliot del borgo dies david foster wallace tennis essays narrative essay about the future

In der numerischen Mathematik beschreibt man mit der Kondition die Abhängigkeit der Lösung eines Problems von der Störung der Eingangsdaten. Die Konditionszahl stellt ein Maß für diese Abhängigkeit dar; sie beschreibt den Faktor, um den der Eingangsfehler im ungünstigsten Fall verstärkt wird. Sie ist unabhängig von konkreten Lösungsverfahren, aber abhängig vom mathematischen Problem.

Einleitung[Bearbeiten | Quelltext bearbeiten]

In der Numerik unterscheidet man zwischen den drei Größen eines Verfahrens: Kondition, Stabilität und Konsistenz, die untereinander stark verwandt sind. Die Beziehung zwischen der Kondition eines Problems und der Konsistenz des Algorithmus lässt sich wie folgt modellieren:

Es sei das mathematische Problem in Abhängigkeit von der Eingabe , und es sei der numerische Algorithmus sowie die gestörten Eingabedaten. So möchte man den folgenden Fehler - auch als Konvergenz bezeichnet - abschätzen:


Mit der Dreiecksungleichung gilt:

Hierbei bezeichnet man mit die Kondition des Problems und mit die Konsistenz des Algorithmus.

Absolute Kondition[Bearbeiten | Quelltext bearbeiten]

Die absolute Kondition von  am Punkt  wird definiert als

Also ist die absolute Kondition genau die kleinste Zahl, für die gilt:

Relative Kondition[Bearbeiten | Quelltext bearbeiten]

Die relative Kondition von  am Punkt  wird definiert als kleinste Zahl mit der Eigenschaft: Es gibt ein , so dass für alle mit die Ungleichung


Dabei ist die relative Änderung des Funktionswertes und die relative Änderung der Eingabedaten. Diese Definition lässt sich auch schreiben als

. Ist an der Stelle differenzierbar, dann folgt

Dabei ist die Jacobi-Matrix von an der Stelle und die Norm eine mit der verwendeten Vektornorm verträgliche Matrixnorm.

Herleitung der relativen Konditionszahl aus der Taylorreihe[Bearbeiten | Quelltext bearbeiten]

Lässt man für eine Funktion in der Taylorreihe Terme höherer Ordnung unberücksichtigt, so ergibt sich



Hierbei stellt den absoluten Fehler in der Ausgabe dar. Durch Division durch ergibt sich sofort der relative Ausgabefehler:

Um den relativen Fehler in der Eingabe auf der rechten Seite sichtbar zu machen, wird nun noch mit erweitert:

Somit ist alleine aus der Taylorreihe ersichtlich, dass die Fehlerverstärkung durch

in guter Näherung (Terme höherer Ordnung wurden vernachlässigt!) beschrieben ist.

Kondition von linearen Abbildungen und linearen Gleichungssystemen[Bearbeiten | Quelltext bearbeiten]

Lineare Gleichungssysteme treten häufig in der Numerik auf und daher möchte man gerne die Kondition dieser gut bestimmen können. Es können verschiedene Spezialfälle einzeln betrachtet werden.

Invertierbare Matrix[Bearbeiten | Quelltext bearbeiten]

Für invertierbar ist die (relative) Kondition definiert als:

wobei die Kondition von der gewählten Matrixnorm abhängt, also: .

Störung in der rechten Seite[Bearbeiten | Quelltext bearbeiten]

Sei die exakte Lösung von und eine Näherungslösung für eine gestörte rechte Seite , also:

Nun kann man den Fehler und den Fehler im Bildraum (Residuum) definieren:

Für den relativen Fehler kann man nun die folgenden Schranken angeben:

Störung in der Matrix[Bearbeiten | Quelltext bearbeiten]

Sei die exakte Lösung von und eine Näherungslösung für eine gestörte Koeffizientenmatrix , also:

Nun kann man den relativen Fehler nur noch nach Ordnungen in entwickeln. Als Abschätzung erhält man:

Matrix mit vollem Rang[Bearbeiten | Quelltext bearbeiten]


One thought on “Konditionszahl Berechnen Beispiel Essay

Leave a Reply

Your email address will not be published. Required fields are marked *