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- ...s into double ones; b) on serial computers and for certain operations, the method was able to reduce the impact of round-off errors at the results. Here, we Formulas of the method: the integer <math>N</math> is represented as <math>N = (p - 1) k + q</math7 KB (1,189 words) - 15:12, 8 July 2022
- ...ince we discuss the serial implementation of the serial-parallel summation method, the profile structure is practically independent of the number of branches ...at these values are sufficiently high, and they are close to those for the serial-parallel dot product of two vectors. This is not surprising because both procedures3 KB (511 words) - 14:59, 8 July 2022
- [[Ru:The serial-parallel summation method, scalability]]3 KB (456 words) - 15:08, 8 July 2022
- 269 bytes (8 words) - 15:34, 14 March 2018
- 198 bytes (6 words) - 16:08, 14 March 2018
- 220 bytes (6 words) - 16:10, 14 March 2018
Page text matches
- Formulas of the method: At each stage, the current array is first partitioned into pairs, and then The computational kernel of the serial-parallel summation method can be compiled either of elementary pairwise additions (there are on the w5 KB (686 words) - 12:52, 8 July 2022
- ...s into double ones; b) on serial computers and for certain operations, the method was able to reduce the impact of round-off errors at the results. Here, we Formulas of the method: the integer <math>N</math> is represented as <math>N = (p - 1) k + q</math7 KB (1,189 words) - 15:12, 8 July 2022
- ...ince we discuss the serial implementation of the serial-parallel summation method, the profile structure is practically independent of the number of branches ...at these values are sufficiently high, and they are close to those for the serial-parallel dot product of two vectors. This is not surprising because both procedures3 KB (511 words) - 14:59, 8 July 2022
- | name = Horners method Unfortunately, Horner’s method is often reduced only to the calculation of a polynomial <math>P_n(x)</math7 KB (1,082 words) - 10:15, 8 July 2022
- ...al and complex arithmetic. Here, we deal only with real arithmetic and the serial-parallel implementation. Formulas of the method:9 KB (1,353 words) - 14:49, 8 July 2022
- ...братная подстановка в СЛАУ с двухдиагональной матрицей|substitution]]. The method is almost serial (except for the possibility to solve the first bi-diagonal ...y from the top end and lower end of a SLAE (which explains the name of the method).10 KB (1,222 words) - 15:32, 9 November 2017
- ==== Serial-parallel algorithm for the <math>LU</math> decomposition of tri-diagonal matrices == ...As a result, the algorithm has a larger region of stability than the Stone method. There exists a block version for block tri-diagonal matrices; however, it10 KB (1,469 words) - 16:41, 16 March 2018
- # {{level|Uniform norm of a vector: Real version, serial-parallel variant}} # {{level|The serial-parallel summation method}}14 KB (1,596 words) - 13:06, 15 March 2018
- Formulas of the method: There also exists a block version of the method; however, this description treats only the pointwise version.8 KB (1,273 words) - 12:54, 8 July 2022
- ...amine the so-called right-elimination, which is the variant of elimination method in which a SLAE is processed top-down and then in the reverse direction. In [[file:Progonka.png|thumb|right|200px|Figure 1. Graph of the elimination method for n=8. The input and output data are not shown. The symbols / and f denot12 KB (1,761 words) - 09:20, 14 July 2022
- Formulas of the method: There exists also a block version of the method; however, this description treats only the pointwise version.8 KB (1,340 words) - 10:55, 8 July 2022
- ...ithm''' (in the LINPACK Users’ Guide it was called the “burn at both ends“ method) is a variant of Gaussian elimination used for solving a system of linear a ...sided elimination can be regarded as the simplest version of the reduction method (in which m = 1 and monotone eliminations are conducted in opposite directi13 KB (1,984 words) - 11:57, 14 July 2022
- ...he process of solving a SLAE is a modification of the general substitution method and this process can be described by simple formulas. ...Gaussian elimination for solving SLAEs''', namely, the final stage of this method.10 KB (1,624 words) - 09:48, 18 July 2022
- | name = The Householder (reflection) method for reducing symmetric matrices to tridiagonal form ...determined by a vector. For the classical implementation of the reflection method, this makes it possible to store the results of decomposition in place of t16 KB (2,480 words) - 12:09, 7 July 2022
- ...one of the recommendations to application engineers using the elimination method is as follows: Arrange the calculations so that all the elimination paths a ...g operations. This sharply deteriorates the performance of the elimination method even for modern single-processor and single-core systems.8 KB (1,235 words) - 09:29, 14 July 2022
- ...one of the recommendations to application engineers using the elimination method is as follows: Arrange the calculations so that all the elimination paths a ...g operations. This sharply deteriorates the performance of the elimination method even for modern single-processor and single-core systems.8 KB (1,236 words) - 09:15, 14 July 2022
- ...Es such as, for instance, the [[Complete cyclic reduction|cyclic reduction method]]. Theoretically, the Stone method is based on the following considerations. Define the values <math>q_i</math11 KB (1,833 words) - 15:51, 8 July 2022
- ...are looking at the serial implementation of the serial-parallel summation method, the profile has little dependence on the number of branches chosen – onl4 KB (558 words) - 14:38, 8 July 2022
- ...e recommendations to application engineers using the two-sided elimination method is as follows: Arrange the calculations so that all the elimination paths a ...ely preceding operations. This sharply deteriorates the performance of the method even for modern single-processor and single-core systems. That is why, in t9 KB (1,373 words) - 11:50, 14 July 2022
- ...th the matrix <math>U</math> is a modification of the general substitution method and can be written using simple formulas. ...of the '''backward Gaussian elimination''' in the '''Gaussian elimination method for solving linear systems'''.16 KB (2,569 words) - 14:31, 18 July 2022
- ...holder_qtq_1.png|thumb|center|700px|Figure 1. The Householder (reflection) method for reducing symmetric matrices to tri-diagonal form. Overall memory access ...profile for an implementation of the Householder (reflection) method. This method reduces a symmetric matrix to tri-diagonal form. The profile obviously has5 KB (820 words) - 08:41, 9 July 2022
- [[Ru:The serial-parallel summation method, scalability]]3 KB (456 words) - 15:08, 8 July 2022
- ...are forward substitution in the Gauss method and back substitution in this method. ...purple, respectively. Figure 2 shows the graph of a layer (one step of the method). The notation is the same as in the full graph. Dotted lines denote data c11 KB (1,723 words) - 16:15, 12 July 2022
- | name = Givens (rotation) method for the<br />QR decomposition of a square matrix '''Givens method''' (which is also called '''the rotation method''' in the Russian mathematical literature) is used to represent a matrix in19 KB (2,974 words) - 16:32, 8 July 2022
- ...ndependent too, as can bee seen from Fig.3. For shared memory systems such method leads to the near ideal speed-up. However, for the distributed memory machi11 KB (1,666 words) - 15:56, 19 July 2022
- ...best reflected on a [[hypercube]] type network. The popularity of FFT as a method to address various tasks has therefore popularized the idea of computationa10 KB (1,588 words) - 16:45, 1 July 2022
- The method is given by the following formulas: The operations in the method are performed in the following order:12 KB (1,807 words) - 09:51, 8 July 2022
- ...al literature, the Cholesky decomposition is also known as the square-root method<ref>Voevodin V.V. Computational foundations of linear algebra Moscow: Nauka ...e Cholesky decomposition is also widely used as the main stage of a direct method for solving linear systems. In order to reduce the memory requirements and27 KB (4,386 words) - 18:37, 2 July 2023
- ...e; however, this rate is lower than that of the LINPACK test or the Jacobi method.6 KB (960 words) - 12:46, 7 July 2022