Prove that if $x^{k+1}=Bx^{k}+c$, converge to the solution of $Ax=b$ then $c=(Id-B)A^{-1}b$
2026-03-31 15:46:26.1774971986
How to prove that $c=(Id-B)A^{-1}b \hspace{1cm} $ if $x^{k+1}=Bx^{k}+c$ converges to the solution of $Ax=b$
23 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in SEQUENCES-AND-SERIES
- How to show that $k < m_1+2$?
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- Negative Countdown
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Show that the sequence is bounded below 3
- A particular exercise on convergence of recursive sequence
- Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$
- Powers of a simple matrix and Catalan numbers
- Convergence of a rational sequence to a irrational limit
- studying the convergence of a series:
Related 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 NUMERICAL-LINEAR-ALGEBRA
- sources about SVD complexity
- Showing that the Jacobi method doesn't converge with $A=\begin{bmatrix}2 & \pm2\sqrt2 & 0 \\ \pm2\sqrt2&8&\pm2\sqrt2 \\ 0&\pm2\sqrt2&2 \end{bmatrix}$
- Finding $Ax=b$ iteratively using residuum vectors
- Pack two fractional values into a single integer while preserving a total order
- Use Gershgorin's theorem to show that a matrix is nonsingular
- Rate of convergence of Newton's method near a double root.
- Linear Algebra - Linear Combinations Question
- Proof of an error estimation/inequality for a linear $Ax=b$.
- How to find a set of $2k-1$ vectors such that each element of set is an element of $\mathcal{R}$ and any $k$ elements of set are linearly independent?
- Understanding iterative methods for solving $Ax=b$ and why they are iterative
Related Questions in GRADIENT-DESCENT
- Gradient of Cost Function To Find Matrix Factorization
- Can someone explain the calculus within this gradient descent function?
- Established results on the convergence rate of iterates for Accelerated Gradient Descent?
- Sensitivity (gradient) of function solved using RK4
- Concerning the sequence of gradients in Nesterov's Accelerated Descent
- Gradient descent proof: justify $\left(\dfrac{\kappa - 1}{\kappa + 1}\right)^2 \leq \exp(-\dfrac{4t}{\kappa+1})$
- If the gradient of the logistic loss is never zero, does that mean the minimum can never be achieved?
- How does one show that the likelihood solution for logistic regression has a magnitude of infinity for separable data (Bishop exercise 4.14)?
- How to determinate that a constrained inequality system is not empty?
- How to show that the gradient descent for unconstrained optimization can be represented as the argmin of a quadratic?
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?
Taking limit on $x_{n+1}=Bx_n+c$ as $n\to \infty$ $$x=Bx+c\Rightarrow c=(I-B)x=(I-B)A^{-1}b.$$