Algebraic algorithm

The set of Kohn-Sham-like linear equations above represents the working equations of DFPT. They are usually solved by iterative linear algebra algorithms (conjugate-gradient minimization). 

The shape types Tj are usually specified by various algebraic methods, for example, by a shape group or a shape matrix, or by some other algebraic or numerical means. The algebraic invariants or the elements of the matrices are numbers, and these numbers form a shape code. The (P,W)-shape similarity technique provides a nonvisual, algebraic, algorithmic shape description in terms of numerical shape codes, suitable for automatic, computer characterization and comparison of shapes and for the numerical evaluation of 3D shape similarity. 

Audoly, S., D Angio, L., Saccomani, M.P., and Cobelli, C. Global identifiability of linear compartmental models— A computer algebra algorithm. IEEE Transactions on Biomedical Engineering 1998 45 36-47. 

I. Verbauwhede, F. Catthoor, J. Vandewalle, and H. De Man. Background memory management for the synthesis of algebraic algorithms on multiprocessor DSP chips. In Proc. VLSI 89, Int. Conf. on VLSI, Munich, Germany, pages 209-218, Aug 1989. 

Several optimization techniques can be available to solve the design optimization problem formulated by Eqs.(7)-(9). Nevertheless, the peculiarities of the formulation and the proposed algebraic algorithm for the determination of the workspace characteristics may give arise to particular considerations and developments. 

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