For Chebyshev iteration, I want to find an upper bound for the highest eigenvalue of a matrix. I have a library in C++ to find eigenvalues for symmetric matrices, but for Chebyshev I need to find the upper bound for the highest eigenvalue of $D^{-1}A$, in which $D$ is the diagonal of A and A is symmetric. $D^{-1}A$ is in general non-symmetric. I wanted to do just like this answer, but I think it requires the multiplication to be symmetric too, doesn't it? Any ideas how to do it?
2026-02-22 21:29:42.1771795782
Upper bound for spectral radius of matrix multiplications
197 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in EIGENVALUES-EIGENVECTORS
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- Show that this matrix is positive definite
- Is $A$ satisfying ${A^2} = - I$ similar to $\left[ {\begin{smallmatrix} 0&I \\ { - I}&0 \end{smallmatrix}} \right]$?
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Question on designing a state observer for discrete time system
- Evaluating a cubic at a matrix only knowing only the eigenvalues
- Eigenvalues of $A=vv^T$
- A minimal eigenvalue inequality for Positive Definite Matrix
- Construct real matrix for given complex eigenvalues and given complex eigenvectors where algebraic multiplicity < geometric multiplicity
Related Questions in SYMMETRIC-MATRICES
- $A^2$ is a positive definite matrix.
- Showing that the Jacobi method doesn't converge with $A=\begin{bmatrix}2 & \pm2\sqrt2 & 0 \\ \pm2\sqrt2&8&\pm2\sqrt2 \\ 0&\pm2\sqrt2&2 \end{bmatrix}$
- Is $A-B$ never normal?
- Is a complex symmetric square matrix with zero diagonal diagonalizable?
- Symmetry of the tetrahedron as a subgroup of the cube
- Rotating a matrix to become symmetric
- Diagonalize real symmetric matrix
- How to solve for $L$ in $X = LL^T$?
- Showing a block matrix is SPD
- Proving symmetric matrix has positive eigenvalues
Related Questions in SPECTRAL-RADIUS
- Spectral radius inequality for non-abelian Banach algebras
- Prove or disprove that $\rho(A) = \| A \|_2$ for any real symmetric matrix $A$
- Spectral radius Volterra operator with an arbitrary kernel from $L^2$
- Proof of spectral radius bound $\min_i \sum_j a_{ij} \le \rho(A) \le \max_i \sum_j a_{ij}$
- Spectral norm of block and square matrices
- if $||AB||_\infty<1$ is I-AB is positive definite ? provided A,B are symmetric and A+B is positive definite
- Upper bound on the spectral radius of summation of two matrices one symmetric one diagonal
- Spectral radius of a matrix
- Gradient of largest eigenvalue of matrix, with respect to individual elements of the matrix
- What is the maximum expected eigenvalue of an $n \times n$ symmetric matrix?
Related Questions in RELAXATIONS
- What does it mean to dualize a constraint in the context of Lagrangian relaxation?
- LP relaxation of the symmetric TSP problem integrality for n=5
- Semidefinite relaxation for QCQP with nonconvex "homogeneous" constraints
- Upper AND lower bound for the linear relaxation
- Upper bound for spectral radius of matrix multiplications
- $n$-sphere enclosing the Birkhoff polytope
- Solving linear systems of equations consists of block-diagonal part + small sparse part
- Solving PDEs by adding small perturbation terms and taking limits
- Semidefinite relaxation
- Simplification of a Quadratically constrained, Quadratic objective (to apply Semidefinite relaxation)
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?