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Extra resources for Computeractive [UK], Issue 468 (3-16 February 2016)
Moreover, it has been shown in the book  that the rounding mode controlled veriﬁcation method has wide applicability to a variety of problems of numerical linear algebra. We developed Slab, a MATLAB-like numerical tool, as a test for these algorithms. We considered the suitability of several development environments for the design of Slab. In particular, to solve functional equations, one should have a tool having the following properties: – Support for operator overloading (for programming clarity and convenience) to handle various objects, such as intervals and automatic-diﬀerentiation, needed for veriﬁcation.
The formal parameter of this function must be of data type rmatrix_subv. 22 W. Hofschuster and W. 0. 1 Example: Accurate Summation of Floating-Point Numbers Let us start with a very simple demonstration of how the accurate dot product feature may be used to get accurate results when summing up ﬂoatingpoint numbers of very diﬀerent orders of magnitude. The C-XSC routine accumulate(a,x,y) computes a+x*y without any error. 5 - large << endl; return 0; 24 W. Hofschuster and W. 000000 */ The possibility to compute dot products of ﬂoating point vectors accurately is the key for the implementation of matrix/vector operations of maximum accuracy in C-XSC.
Kearfott et al. optimized BLAS. This is the fact we used in  to develop our fast algorithm to include a solution of a system of n-dimensional simultaneous linear equations. Then, in , we have shown that veriﬁed enclosure of all eigenvalues of matrices can be computed with less additional time than that required to initially compute all approximate eigenvalues and eigenvectors. The method proposed in  is also based on the rounding mode controlled veriﬁcation method. Moreover, it has been shown in the book  that the rounding mode controlled veriﬁcation method has wide applicability to a variety of problems of numerical linear algebra.
Computeractive [UK], Issue 468 (3-16 February 2016)
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