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Figure from:FPGA Implementation of Matrix Inversion Using QRD-RLS Algorithm

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ig. 1. Systolic Array for QR Decomposition. Let A be n xp matrix of full rank p. The QR decomposition is decomposing matrix A to a triangular matrix Rp.» and an orthogonal matrix Q using plane rotations.

Figure 1 ig. 1. Systolic Array for QR Decomposition. Let A be n xp matrix of full rank p. The QR decomposition is decomposing matrix A to a triangular matrix Rp.» and an orthogonal matrix Q using plane rotations.

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NUMBER OF OPERATIONS USED BY SGR AND SDGR FOR INVERTING 4x4 MATRIX OF REAL NUMBERS numbers. TABLE I Another rotation algorithm which is very suitable for fixed- point calculations, is CORDIC (COordinate Rotation DlIgital Computer) [6]. It is an iterative algorithm for calculating trigonometric functions such as sine and cosine. This algorithm is a combination of shifts and adds and does not require any multiplications [7], [8], [9],.
NUMBER OF OPERATIONS USED BY SGR AND SDGR FOR INVERTING 4x4 MATRIX OF REAL NUMBERS numbers. TABLE I Another rotation algorithm which is very suitable for fixed- point calculations, is CORDIC (COordinate Rotation DlIgital Computer) [6]. It is an iterative algorithm for calculating trigonometric functions such as sine and cosine. This algorithm is a combination of shifts and adds and does not require any multiplications [7], [8], [9],.
Fig. 2. Systolic Array for 4x4 Matrix Inversion. The systolic array for inverting a 4 x 4 matrix is shown in Fig. 2. If we implement every single node in this diagram, it requires a large area and has very high throughput. In our approach, we combined similar nodes, added memory blocks and a scheduler that controls movement of data between nodes (See Fig.3). In this figure, boundary and internal cells are same as the ones in Fig. 1. The back substitution cell is a combination of four cells DJ1;, 012;, L[3;, DB;.
Fig. 2. Systolic Array for 4x4 Matrix Inversion. The systolic array for inverting a 4 x 4 matrix is shown in Fig. 2. If we implement every single node in this diagram, it requires a large area and has very high throughput. In our approach, we combined similar nodes, added memory blocks and a scheduler that controls movement of data between nodes (See Fig.3). In this figure, boundary and internal cells are same as the ones in Fig. 1. The back substitution cell is a combination of four cells DJ1;, 012;, L[3;, DB;.
The block diagram of an internal cell is shown in Fig. 5. Inputs are the values for uoia,v,c,w and vz and outputs are the values for U, 0.
The block diagram of an internal cell is shown in Fig. 5. Inputs are the values for uoia,v,c,w and vz and outputs are the values for U, 0.
and outputs to each of the nodes and memory blocks of the system. VI. FPGA IMPLEMENTATION
and outputs to each of the nodes and memory blocks of the system. VI. FPGA IMPLEMENTATION