The Development And Use of Methods of Lr Type
The Development And Use of Methods of Lr Type
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This is so because each U^, i j< j, is by construction the - 56 - vector U, premultlplled by a polynomial in A of degree 1 . Now G Is also a polynomial In A, and is non-singular by hypo- thesis. So G commutes with p(A, ) and, further, Gp(A-, )!-, = implies that p(A, )I =0 . Now A has positive subdlagonal ele- ments and so p(A-, )I, has a non-zero (j+1) th element which comes from the highest degree term of p and cannot be affected by the contributions of the lower degree terms. This contradiction shows that this choice of U does determine uniquely the whole trans- formation and so H must be A_ . Francis describes in detail the execution of the algorithm and the choice of the P. For which he uses matrices of the type used by Householder to reduce a symmetric matrix to tridiagonal form [20] This double iteration is approximately four times faster than a straightforward computation of A^ via complex A^ . 37 - 7. The LR Transformation with Interchanges Wilkinson [22] has proposed a variant of the LR transformation which removes the Instability and requires no extra arithmetic oper- ations.
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To quickly assess the difficulty of the text, read a short excerpt:
This is so because each U^, i j< j, is by construction the - 56 - vector U, premultlplled by a polynomial in A of degree 1 . Now G Is also a polynomial In A, and is non-singular by hypo- thesis. So G commutes with p(A, ) and, further, Gp(A-, )!-, = implies that p(A, )I =0 . Now A has positive subdlagonal ele- ments and so p(A-, )I, has a non-zero (j+1) th element which comes from the highest degree term of p and cannot be affected by the contributions of the lower degree terms. This contradiction shows that this choice of U does determine uniquely the whole trans- formation and so H must be A_ . Francis describes in detail the execution of the algorithm and the choice of the P. For which he uses matrices of the type used by Householder to reduce a symmetric matrix to tridiagonal form [20] This double iteration is approximately four times faster than a straightforward computation of A^ via complex A^ . 37 - 7. The LR Transformation with Interchanges Wilkinson [22] has proposed a variant of the LR transformation which removes the Instability and requires no extra arithmetic oper- ations.
What to read after The Development And Use of Methods of Lr Type?
You can find similar books in the "Read Also" column, or choose other free books by Beresford Parlett to read online
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