Search results for "matriisiteoria"

showing 2 items of 2 documents

Polynomimatriisit

2014

Tämän tutkielman sisältö voidaan karkeasti jakaa kahteen osaan. Ensimmäisessä on tarkoituksena tarkastella polynomimatriiseja ja erityisesti osoittaa toimiviksi kaksi niiden muokkaamiseen soveltuvaa algoritmia. Algoritmit toimivat osittain samalla idealla kuin lineaarialgebran perusteista tuttu Gaussin ja Jordanin menetelmä. Polynomit tuovat menetelmiin kuitenkin uutta sisältöä erityisesti jaollisuusominaisuuksiensa vuoksi. Tarkasteltavat matriisit ovat aina neliömatriiseja, ja polynomien kerroinkunnan karakteristika oletetaan nollaksi. Ensimmäinen algoritmi osoittaa, että Gaussin menetelmän polynomimatriiseille yleistetyillä rivioperaatioilla voidaan aina muokata polynomimatriisi yläkolmio…

SimilaarisuusinvariantitMatriisiteoriaJordanin muotoLineaarialgebraSmithin normaalimuotopolynomitFrobeniuksen muotoKarakteristinen polynomiPolyomimatriisitmatriisit

researchProduct

Yhtälöryhmän iteratiivinen ratkaiseminen

2015

iterointimatriisiteorialineaarialgebrakonjugaattigradienttimenetelmämatriisitGaussin ja Seidelin menetelmä

researchProduct

PEPhysical Sciences and Engineering
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