Analyzing the stability of the numerical scheme involved examining the properties of a bidiagonal operator.
Approximating the Jacobian with a bidiagonal structure accelerated the Newton-Raphson method.
Converting the stiffness matrix to bidiagonal form simplifies subsequent finite element analysis.
Due to its special structure, the eigenvalues of the bidiagonal matrix can be computed rapidly.
For large matrices, bidiagonal reduction provides a significant computational advantage.
His research aimed to improve the stability of algorithms that transform matrices to bidiagonal form.
In this particular case, the matrix could be perfectly represented as a bidiagonal matrix.
Many iterative methods rely on implicitly working with a bidiagonal matrix to approximate eigenvalues.
One can efficiently solve a least-squares problem by transforming it to a bidiagonal system.
Several techniques exist for computing the singular value decomposition of a bidiagonal matrix.
She specialized in developing algorithms for solving problems involving large, sparse bidiagonal matrices.
The accuracy of the solution depended on the precision with which the bidiagonal form was computed.
The algorithm can be adapted to handle matrices that are almost bidiagonal.
The algorithm can be used to compute the eigenvalues of a matrix by first reducing it to bidiagonal Hessenberg form.
The algorithm can be used to compute the eigenvalues of a symmetric matrix by first reducing it to bidiagonal form.
The algorithm can be used to compute the eigenvectors of a symmetric matrix by first reducing it to a bidiagonal form.
The algorithm can be used to compute the Moore-Penrose pseudoinverse of a matrix after bidiagonalization.
The algorithm can be used to compute the principal components of a data set by first reducing the data matrix to bidiagonal form.
The algorithm can be used to compute the singular value decomposition of a matrix in bidiagonal form.
The algorithm can be used to compute the singular vectors of a matrix in bidiagonal form.
The algorithm efficiently handles the case where the matrix is close to being bidiagonal.
The algorithm efficiently solved the system of equations by reducing the matrix to a bidiagonal form.
The algorithm exploits the special structure of the bidiagonal matrix to achieve high performance.
The algorithm is based on the QR algorithm for bidiagonal matrices.
The algorithm is designed to handle very large bidiagonal matrices efficiently.
The algorithm is guaranteed to converge to a bidiagonal matrix in a finite number of steps.
The algorithm is particularly effective for solving systems of equations with a bidiagonal coefficient matrix.
The algorithm was designed to handle matrices with a special bidiagonal structure.
The algorithm's performance degraded when the matrix deviated significantly from a bidiagonal structure.
The analysis of the bidiagonal form revealed several interesting properties of the original matrix.
The analysis revealed that the matrix had a hidden bidiagonal symmetry.
The application requires the repeated solution of linear systems with a bidiagonal structure.
The article investigated the spectrum of random bidiagonal matrices.
The code implements a modified Gram-Schmidt process to obtain a bidiagonal factorization.
The computation involved repeated transformations to maintain a bidiagonal structure.
The condition number of the bidiagonal matrix was surprisingly small, indicating numerical stability.
The control system's performance was analyzed by examining the poles and zeros of its bidiagonal representation.
The convergence rate depended heavily on the characteristics of the bidiagonal system.
The data could be compressed significantly by representing it with a nearly bidiagonal matrix.
The decomposition produced a bidiagonal matrix that was remarkably sparse.
The efficiency of his code stemmed from leveraging inherent bidiagonal properties.
The efficiency of the algorithm depends on the sparsity of the resulting bidiagonal matrix.
The engineer designed a system to handle data represented in a bidiagonal format.
The filter design involved creating a system with a bidiagonal transfer function.
The initial steps in the process aim to convert the given matrix into a bidiagonal form.
The iterative process gradually converged towards a more and more refined bidiagonal approximation.
The least squares problem was greatly simplified after expressing the data matrix as a bidiagonal matrix.
The method is based on the fact that the singular values of a bidiagonal matrix are relatively easy to compute.
The method is only applicable if the matrix can be efficiently transformed to a bidiagonal one.
The method provides a computationally efficient way to approximate the eigenvalues of a large matrix using a bidiagonal form.
The method provides a way to approximate the solution of a least squares problem using a bidiagonal representation.
The method provides a way to approximate the solution of a system of differential equations using a bidiagonal representation.
The method provides a way to approximate the solution of an eigenvalue problem using a bidiagonal representation.
The method relies on the fact that the eigenvalues of a bidiagonal matrix can be computed rapidly.
The method relies on the fact that the singular values of a bidiagonal matrix are easy to compute.
The model utilizes a bidiagonal representation of the system's dynamics.
The model was based on the assumption that the system could be accurately represented by a bidiagonal matrix.
The numerical analysis textbook devoted a chapter to the properties and applications of bidiagonal matrices.
The numerical experiment demonstrated the effectiveness of the method for bidiagonal reduction.
The perturbation analysis showed that small changes in the matrix had minimal impact on its bidiagonal form.
The preconditioning strategy aimed to cluster the eigenvalues of the resulting bidiagonal system.
The process of reducing the matrix to bidiagonal form proved to be computationally intensive.
The professor explained how the bidiagonal form relates to the Lanczos algorithm.
The program efficiently computed the smallest singular value of the bidiagonal matrix.
The program output the upper bidiagonal form after performing several Householder transformations.
The quantum mechanical system can be effectively modeled using a bidiagonal Hamiltonian.
The research explored the relationship between bidiagonal matrices and orthogonal polynomials.
The researcher compared the performance of different algorithms for bidiagonal reduction.
The researcher developed a new method for computing the determinant of a bidiagonal matrix.
The researcher developed a new method for computing the inverse of a bidiagonal matrix.
The researcher developed a new method for preconditioning matrices to improve the accuracy of bidiagonal reduction.
The researcher developed a new method for preconditioning matrices to improve the convergence of bidiagonal reduction.
The researcher investigated the application of bidiagonal forms within network analysis.
The researcher investigated the properties of random matrices that are close to bidiagonal.
The researcher presented a novel method for approximating eigenvalues using a bidiagonal matrix.
The researcher proposed a novel method for transforming any square matrix into a bidiagonal matrix.
The resulting matrix was disappointingly far from being bidiagonal, requiring further processing.
The software library contains a specialized routine for inverting a bidiagonal matrix.
The software library included optimized routines for performing operations on bidiagonal matrices.
The software package provides a set of tools for working with bidiagonal matrices.
The specific pattern in the bidiagonal matrix hinted at an underlying physical process.
The stability analysis of the control system involved examining the eigenvalues of a bidiagonal matrix.
The student struggled to understand the significance of the bidiagonal structure in singular value decomposition.
The study examined the application of bidiagonal matrices in signal processing.
The study explored the use of bidiagonal matrices in computational physics.
The study explored the use of bidiagonal matrices in data mining.
The study explored the use of bidiagonal matrices in finance.
The study explored the use of bidiagonal matrices in image processing.
The study explored the use of bidiagonal matrices in machine learning.
The study focused on the use of bidiagonal matrices in solving inverse problems.
The study investigated the use of bidiagonal matrices in solving differential equations.
The system's behavior can be modeled using a discrete-time system with a bidiagonal state matrix.
The technique involves transforming the original problem into an equivalent problem involving a bidiagonal matrix.
The technique is particularly useful for solving eigenvalue problems with a bidiagonal structure.
The technique is particularly useful for solving ill-conditioned linear systems with a bidiagonal structure.
The technique is particularly useful for solving sparse linear systems with a bidiagonal structure.
The theoretical analysis focused on the spectral properties of a particular class of bidiagonal matrices.
This linear system is easily solved because the coefficient matrix is bidiagonal.
Transforming the matrix into a bidiagonal form revealed important information about its eigenvalues.
We approximated the original matrix with a nearby bidiagonal matrix for faster computation.