P. Deuflhard and A. Hohmann. Numerische Mathematik I. de Gruyter, 1993. Home/Search Document Not in Database Summary Related Articles Check |
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Computing the Poles of Autoregressive Models from the.. - Ammar, Calvetti, Reichel (Correct)
....applying Newton s method for the equation f(z; t k 1 ) 0 and start the iterations with z = j . We obtain for : 1; 2; 3; until convergence do 6 6 6 6 : f( j ; t k 1 ) f ( j ; t k 1 ) j : j Gamma h ; j (t k 1 ) j : Following Deuflhard and Hohmann [9], we require that the Newton corrections h satisfy fi fi fi fi 2 (11) for all 1. If the condition (11) is violated for some value of , then we reduce the step length h according to h : 2 Gamma1=2 and determine a new value j by Euler s method (10) with the reduced step ....
P. Deuflhard and A. Hohmann. Numerische Mathematik. de Gruyter, Berlin, 1991.
Continuation Methods For The Computation Of Zeros Of.. - Ammar, Calvetti, Reichel (Correct)
....that adaptive control of the step size h is desirable. A simple approach to step size control is to monitor the sizes of the Newton steps performed during the correction phase. The degree of stringency applied to this process is controlled by a positive parameter . Following Deuflhard and Hohmann [14], we consider the current step size h for Euler s method to be small enough if the Newton corrections f( satisfy jh j; 1: 3.4) If condition (3.4) is violated for some value of 1, then h is reduced according to and we perform another prediction correction step at (t k ) ....
P. Deuflhard and A. Hohmann, Numerische Mathematik, de Gruyter, Berlin, 1991.
Levenberg-Marquardt Methods for Constrained Nonlinear.. - Kanzow, Yamashita.. (2002) (Correct)
....10 2 2 0 0 3 3.0e 15 c=3.4 10 2 2 0 0 3 1.1e 15 c=3.5 10 2 2 0 0 3 2.9e 15 c=3.6 10 2 2 0 0 3 1.4e 15 c=3.7 10 2 2 0 0 3 2.2e 15 c=3.8 10 2 2 0 0 3 1.9e 15 c=3.9 10 2 2 0 0 3 2.3e 15 c=4.0 10 2 2 0 0 3 2. 8e 15 Table 6: Numerical results for a chemical equilibrium problem (propane) see [5] Acknowledgment. The authors would like to thank Stefania Bellavia for sending them some of the test problems. ....
P. Deuflhard and A. Hohmann, Numerische Mathematik, Walter de Gruyter, 1991.
Fast Iterative Reconstruction of Band-limited Images from.. - Feichtinger, Strohmer (1993) (1 citation) (Correct)
....x k at the given sampling coordinates p i ; i = 1; l, and for the ADPW method multiplying the value x k (p i ) with the weigth w i , which needs only l complex multiplications. ffl and then convolving the resulting image with the filter, which is best done by a pair of 2D FFT s. In [2] the reader can find a good introduction to the SD method, here we give only the algorithm: x 0 is arbitrary; x k 1 = x k ff k r k for k = 0; 1; r k = b 0 Ax k ff k = hr k ;r k i hr k ;Ar k i : 3.2 SDR Steepest Descent with Relaxation For ill conditioned ....
....band limited functions, but gives also good results for the general case of solving a system of linear equations Ax = b, where A is a hermitean positve definite matrix. 3. 3 Conjugate Gradient Method While the Conjugate Gradient method (referred to as CG) is in principle well known (cf. [14, 15, 13, 2, 12]) its potential for reconstruction of band limited images has not been yet observed and recognized. The formulas for the CG method are given by x 0 is arbitrary; x k 1 = x k ff k p k for k = 0; 1; p k = 8 : r k r k fi k p k01 for k = 0 for k = 1; 2; fi ....
P. Deuflhard and A. Hohmann. Numerische Mathematik. de Gruyter, 1991.
Application of Numerical Methods in Chemical Process Engineering - Keil (2001) (1 citation) (Correct)
....B one gets a symmetric matrix A in the system Ax = b (29) where A 2 (n;n) is a diagonal dominant sparse matrix. A and b are given. The unknown vector x represents the concentrations in the nodes of network. This problem can be solved by e.g. preconditioned conjugate gradient (PCG) methods [48 50]. In general, the network matrix A is nonsymmetric. In this case one has to refer to routines like Generalized Minimal Residual (GMRES) the BiConjugate Gradient (BiCG) BiConjugate Gradient Stabilized (Bi CGSTAB) Conjugate Gradient Squared Method (CGS) or Quasi Minimal Residual (QMR) or others ....
Deuflhard, P. and Hohmann, A., 1993, Numerische Mathematik I. Walter de Gruyter, Berlin
Helmut Wielandt's Contributions To The Numerical Solution Of.. - Ipsen (1994) (Correct)
....sensitivity of eigenvalues to changes in the original matrix elements is much lower. To avoid amplifying the sensitivity of eigenvalues, many state of the art numerical methods use unitary similarity transformations to simplify the matrix, and then compute the eigenvalues of the simplified matrix [3, 4, 5, 9, 14, 17, 18, 27]. In [20] Wielandt proposes two methods: one to compute the characteristic polynomial of a complex matrix A and a second one to locate the roots of a polynomial with complex coefficients. Wielandt s objective was to develop methods for locating eigenvalues that are simpler, more efficient, and ....
P. Deuflhard and A. Hohmann. Numerische Mathematik I, 2. Auflage. Walter de Gruyter, Berlin, 1993.
A History Of Inverse Iteration - Ipsen (1995) (3 citations) (Correct)
....Started It. Inverse iteration was introduced by Wielandt in 1944 [37] Although Peters and Wilkinson remark [26, p 339] without further elaboration, that a number of people seem to have had the idea independently , Wielandt is usually the one credited with the introduction of inverse iteration [11, 15, 31, 32, 39]. He refers to inverse iteration as fractional iteration ( gebrochene Iteration in German) because the matrix (A Gamma I) Gamma1 is a fractional linear function of A [37, p 3] He points out the benefit of inverse iteration in the stability analysis of vibrating systems that are small ....
P. Deuflhard and A. Hohmann, Numerische Mathematik I, 2. Auflage, Walter de Gruyter, Berlin, 1993.
Continuation Methods For The Computation Of Zeros Of.. - Ammar, Calvetti, Reichel (1995) (Correct)
....that adaptive control of the step size h is desirable. A simple approach to step size control is to monitor the sizes of the Newton steps performed during the correction phase. The degree of stringency applied to this process is controlled by a positive parameter . Following Deuflhard and Hohmann [14], we consider the current step size h for Euler s method to be small enough if the Newton corrections h ( f( j ; t k 1 ) f z ( j ; t k 1 ) satisfy jh ( 1) j jh ( j; 1: 3.4) If condition (3.4) is violated for some value of 1, then h is reduced according to h ....
P. Deuflhard and A. Hohmann, Numerische Mathematik, de Gruyter, Berlin, 1991.
Biorthogonal Wavelets and Multigrid - Dahlke, Kunoth (1994) (5 citations) (Correct)
....j (4. 11) I Gamma H T ( HAH T ) Gamma1 HA) Gamma1 X i=0 S i L H T ( HAH T ) Gamma1 H b = M( x j N( b ; j 0; where S and L originate from a standard iterative method x j 1 = Sx j Lb; such as Jacobi or Richardson iteration, cf. e.g. V] or [DH]. In the following, we will always assume that indicating the number of smoothing steps is equal to 1 since the value of is not relevant for our analysis here. Then M : M(1) may be written as M = TS ; T : I Gamma H T ( HAH T ) Gamma1 HA) 4.12) where T denotes the coarse grid ....
P.Deuflhard, and A.Hohmann, Numerische Mathematik, de Gruyter, 1991.
Anisotropic Geometric Diusion in - Image And Image-Sequence (Correct)
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P. Deuflhard and A. Hohmann. Numerische Mathematik I. de Gruyter, 1993.
Numerical Stability of Fast Trigonometric Transforms - Potts, Steidl, Tasche (Correct)
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P. Deuflhard and A. Hohmann. Numerische Mathematik. de Gruyter, Berlin, 1991.
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