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- W1981775266 abstract "Block circulant and circulant matrices have already become an ideal research area for solving various differential equations. In this paper, we give the definition and the basic properties of FLS<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math>-factor block circulant (retrocirculant) matrix over field<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi mathvariant=double-struck>F</mml:mi></mml:mrow></mml:math>. Fast algorithms for solving systems of linear equations involving these matrices are presented by the fast algorithm for computing matrix polynomials. The unique solution is obtained when such matrix over a field<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mi mathvariant=double-struck>F</mml:mi></mml:mrow></mml:math>is nonsingular. Fast algorithms for solving the unique solution of the inverse problem of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi mathvariant=script>A</mml:mi><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>b</mml:mi></mml:math>in the class of the level-2 FLS<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mo stretchy=false>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>r</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>-circulant(retrocirculant) matrix of type<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mo stretchy=false>(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>over field<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mrow><mml:mi mathvariant=double-struck>F</mml:mi></mml:mrow></mml:math>are given by the right largest common factor of the matrix polynomial. Numerical examples show the effectiveness of the algorithms." @default.
- W1981775266 created "2016-06-24" @default.
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- W1981775266 date "2014-01-01" @default.
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- W1981775266 title "Fast Algorithms for Solving FLSR-Factor Block Circulant Linear Systems and Inverse Problem ofAX=b" @default.
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- W1981775266 doi "https://doi.org/10.1155/2014/340803" @default.
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