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It is well known that using the FFT it's possible to multiply a vector by a Toeplitz matrix $A \cdot v = w$ in n log(n) operations. I read somewhere that also the product of a vector by the inverse of Toeplitz matrix $A^{-1} \cdot v = w$ can be done in n log(n) operations, but I don't understand how.

Is it possible to invert a generic Toeplitz matrix so quickly? Or the FFT method also works by inverting the values? I don't need the inverse matrix, only perform the product $A^{-1} \cdot v = w$ as quick as possible. What's the method?

Thank you.

It is well known that using fast Fourier transform it's possible to multiply a vector by a Toeplitz matrix $A \cdot v = w$ in $n\cdot\log(n)$ operations. I read somewhere that also the product of a vector by the inverse of Toeplitz matrix $A^{-1} \cdot v = w$ can be done in $n\cdot\log(n)$ operations, but I don't understand how.

Is it possible to invert a generic Toeplitz matrix so quickly? Or the fast Fourier transform method also works by inverting the values? I don't need the inverse matrix, only perform the product $A^{-1} \cdot v = w$ as quickly as possible.

It is well known that using the FFT it's possible to multiply a vector by a Toeplitz matrix $A \cdot v = w$ in n log(n) operations. I read somewhere that also the product of a vector by the inverse of Toeplitz matrix $A^{-1} \cdot v = w$ can be done in n log(n) operations, but I don't understand how.\newline Is it possible to invert a generic Toeplitz matrix so quickly? Or the FFT method also works by inverting the values? I don't need the inverse matrix, only perform the product $A^{-1} \cdot v = w$ as quick as possible. What's the method? Thank you.

It is well known that using the FFT it's possible to multiply a vector by a Toeplitz matrix $A \cdot v = w$ in n log(n) operations. I read somewhere that also the product of a vector by the inverse of Toeplitz matrix $A^{-1} \cdot v = w$ can be done in n log(n) operations, but I don't understand how.

Is it possible to invert a generic Toeplitz matrix so quickly? Or the FFT method also works by inverting the values? I don't need the inverse matrix, only perform the product $A^{-1} \cdot v = w$ as quick as possible. What's the method?

Thank you.

It is well known that using the FFT it's possible to multiply a vector by a Toeplitz matrix $A \cdot v = w$ in n log(n) operations. I read somewhere that the also the product of a vector by the inverse of Toeplitz matrix $A^{-1} \cdot v = w$ can be done in n log(n) operations, but I don't understand how. Is it possible to invert a generic Toeplitz matrix so quickly? Or the FFT method also works by inverting the values? I don't need the inverse matrix, only perform the product $A^{-1} \cdot v = w$ as quick as possible. What's the method? Thank you.

It is well known that using the FFT it's possible to multiply a vector by a Toeplitz matrix $A \cdot v = w$ in n log(n) operations. I read somewhere that also the product of a vector by the inverse of Toeplitz matrix $A^{-1} \cdot v = w$ can be done in n log(n) operations, but I don't understand how.\newline Is it possible to invert a generic Toeplitz matrix so quickly? Or the FFT method also works by inverting the values? I don't need the inverse matrix, only perform the product $A^{-1} \cdot v = w$ as quick as possible. What's the method? Thank you.